Model auxiliary calibration estimation method and device, electronic equipment and medium

Abstract

The invention relates to a model-assisted calibration estimation method and device, electronic equipment and a medium, and belongs to the technical field of data processing.The method comprises the steps that non-probability samples are extracted from a target population, and a multiple linear regression model between research variables and covariables of the non-probability samples is established; model parameters in the multiple linear regression model are estimated, and estimation of the research variables is obtained based on the estimated model parameters; obtaining a diagonal matrix corresponding to an original weight of a sample unit in the non-probability sample; obtaining a KL distance between the diagonal matrix and a preset calibration weight; constructing a calibration constraint condition of a target calibration weight based on the estimation of the research variable; the calibration weight is calibrated with the minimum KL distance under the calibration constraint condition to obtain a target calibration weight; and determining an estimation result of a total mean value of the target calibration weights based on the target calibration weights. According to the invention, the calibration estimation effect of the non-probability sample is improved.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a model-aided calibration estimation method, apparatus, electronic device, and medium. Background Technology

[0002] With the development of big data and the internet, online surveys have become increasingly popular in the context of big data, and have become an important sampling survey method that is widely used in market research, opinion polls, academic research and other fields.

[0003] However, most online survey samples are non-probability samples, with unknown inclusion probabilities, making it difficult to use them to make statistical inferences about the population. How to make statistical inferences about the population based on non-probability samples has become a hot topic in today's world.

[0004] Currently, methods for estimating the population from non-probability samples can be broadly categorized into two types based on whether or not the samples are assumed to originate from a superpopulation model: pseudo-design-based estimation methods and model-based estimation methods. If the target variable of a finite population is treated as a fixed value, and the method estimates the inclusion probability of non-probability samples from this finite population to infer the population, this is a pseudo-design-based estimation method. If it is assumed that the finite population originates from an infinite superpopulation, and its target variable is treated as a random variable, and the method infers the population by building a superpopulation model of the target variable, this is a model-based estimation method.

[0005] There is relatively little existing research on model-aided calibration estimation methods for non-probable samples. Only Chen et al. (2018) discussed model-aided calibration estimation for non-probable samples using chi-square distance; Pan et al. (2021) explored model-aided SCAD and ALASSO calibration methods for non-probable samples using chi-square distance; and Wang et al. (2025) explored a fusion inference method for non-probable and probable samples in Adaptive LASSO model-aided calibration using chi-square distance. However, Wu and Lu (2016) have demonstrated that calibration estimation under modified backward Kullback-Leibler distance performs better than calibration estimation under chi-square distance. Liu et al. (2024) compared the calibration estimation performance for non-probable samples at different distances, but did not explore calibration estimation under modified backward Kullback-Leibler distance.

[0006] Therefore, in the existing technology, there is a lack of a model-aided calibration estimation for non-probability samples under the modified backward Kullback-Leibler distance, so as to improve the calibration estimation effect of non-probability samples. Summary of the Invention

[0007] In view of this, it is necessary to provide a model-assisted calibration estimation method, device, electronic device and medium to achieve the purpose of calibration estimation effect for non-probability samples.

[0008] To achieve the above objectives, in a first aspect, the present invention provides a model-assisted calibration estimation method, comprising: Non-probability samples are extracted from the target population, and a multiple linear regression model is established between the research variables and covariates of the non-probability samples. The model parameters in the multiple linear regression model are estimated to obtain the estimated model parameters, and the estimated research variables are obtained based on the estimated model parameters. Obtain the diagonal matrix corresponding to the original weights of the sample units in the non-probability sample. The original weights are obtained based on the sampling probability of the sample units. Obtain the Kullback-Leibler distance between the diagonal matrix and the preset calibration weights; The calibration constraints for the target calibration weights are constructed based on the estimation of the research variables. Under calibration constraints, the target calibration weights are obtained by calibrating the calibration weights with the minimum Kullback-Leibler distance. The estimated result of determining the overall mean of the target calibration weights based on the target calibration weights.

[0009] In one possible implementation, the expression for the multiple linear regression model is: ; ; ; In the formula, Indicates the research variable, Represent covariates; This represents the parameters of the multiple linear regression model. ; Indicates the error term , , .

[0010] In one possible implementation, estimating the model parameters in the multiple linear regression model to obtain the estimated model parameters includes: The model parameters in the multiple linear regression model are estimated using the penalized regression algorithm, and the estimated model parameters are obtained.

[0011] In one possible implementation, the estimation of model parameters in the multiple linear regression model based on the penalized regression algorithm to obtain the estimated model parameters includes: Obtain the penalty function of the penalized regression algorithm, and the sum of squared covariances of the research variables; The Lagrange algorithm is used to find the target model parameters that minimize the sum of squared covariances of the research variables under the constraint of the penalty function. The target model parameters are estimated to obtain the estimated model parameters.

[0012] In one possible implementation, the calibration constraints for constructing the target calibration weights based on the estimation of the research variables include: Obtain the constraints on the magnitude of the target calibration weights and the constraints on the estimation of the research variables; The size constraints and the estimated constraints of the studied variables are used as calibration constraints for the target calibration weights.

[0013] In one possible implementation, the step of calibrating the target calibration weights by minimizing the Kullback-Leibler distance under calibration constraints includes: The target calibration weights are obtained by calibrating the calibration weights with the minimum Kullback-Leibler distance under calibration constraints using the Lagrange method.

[0014] In one possible implementation, the expression for estimating the population mean is:

[0015] In the formula, This represents an estimate of the population mean. Let represent the total number of units in the target population, i represent the i-th sample unit, and S represent the non-probability sample. Indicates the research variable, The constraint function representing the covariates. Represents the Lagrange parameters. Indicates the overall target. This represents the initial weight of sample unit i. This represents the model parameters obtained from the penalized regression algorithm.

[0016] Secondly, the present invention also provides a model-aided calibration estimation device, comprising: The multiple linear regression model building module is used to extract non-probability samples from the target population and build a multiple linear regression model between the research variables and covariates of the non-probability samples. The module for estimating and obtaining research variables is used to estimate the model parameters in the multiple linear regression model, obtain the estimated model parameters, and then obtain the estimate of the research variables based on the estimated model parameters. The diagonal matrix acquisition module is used to obtain the diagonal matrix corresponding to the original weights of sample units in non-probability samples. The original weights are obtained based on the sampling probability of the sample units. The distance acquisition module is used to obtain the Kullback-Leibler distance between the diagonal matrix and the preset calibration weights; The constraint determination module is used to construct calibration constraints for the target calibration weights based on the estimation of the research variables. The target calibration weight determination module is used to calibrate the calibration weights to the minimum of the Kullback-Leibler distance under calibration constraints to obtain the target calibration weights; The overall mean estimation module is used to determine the overall mean of the target calibration weights based on the target calibration weights.

[0017] Thirdly, the present invention also provides an electronic device, including a memory and a processor, wherein, The memory is used to store programs; The processor, coupled to the memory, is used to execute the program stored in the memory to implement the steps in the model-aided calibration estimation method described in any of the above implementations.

[0018] Fourthly, the present invention also provides a computer-readable storage medium for storing a computer-readable program or instructions, which, when executed by a processor, can implement the steps in the model-aided calibration estimation method described in any of the above implementations.

[0019] The beneficial effects of this invention are as follows: This invention provides a model-assisted calibration estimation method, comprising: extracting non-probability samples from the target population and establishing a multiple linear regression model between the research variables and covariates of the non-probability samples. Through the multiple linear regression model, the linear relationship between the research variables and covariates can be quantified, providing a basic model for subsequent calibration. The model parameters in the multiple linear regression model are estimated to obtain the estimated model parameters. Based on the estimated model parameters, the research variables are estimated. Through parameter estimation, the predicted values ​​of the research variables can be obtained, which is the basis for subsequent calibration weights. The diagonal matrix corresponding to the original weights of the sample units in the non-probability samples is obtained. The original weights are obtained based on the sampling probability of the sample units. The Kullback-Leibler distance between the diagonal matrix and the preset calibration weights is obtained. By calculating the KL distance between the original weights and the preset calibration weights, the difference between the two can be quantified, providing an optimization target for subsequent calibration. The KL distance is chosen because it effectively measures the difference between two probability distributions, ensuring that the calibrated weights are closer to the preset calibration weights. Calibration constraints for the target calibration weights are constructed based on the estimation of the research variables. Under these constraints, the calibration weights are calibrated using the minimum Kullback-Leibler distance to obtain the target calibration weights. The estimated population mean of the target calibration weights is then determined based on these target calibration weights. This invention calibrates non-probability samples using a modified KL distance, significantly improving model calibration accuracy and generalization ability. It is particularly suitable for small sample or non-probability data scenarios, effectively mitigating the bias problem of traditional KL distance, making model predictions closer to the true distribution, and improving the calibration estimation effect for non-probability samples. Attached Figure Description

[0020] Figure 1 A flowchart illustrating an embodiment of the model-assisted calibration estimation method provided by the present invention; Figure 2 In one embodiment of the model-assisted calibration estimation method provided by the present invention, a mean square error plot of the population mean estimation with different sample sizes is shown. Figure 3 A schematic flowchart of an embodiment of the model-aided calibration estimation device provided by the present invention; Figure 4 A schematic diagram of an embodiment of the electronic device provided by the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0022] In the description of the embodiments of the present invention, unless otherwise stated, "multiple" means two or more. "And / or" describes the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can represent three situations: A exists alone, A and B exist simultaneously, and B exists alone.

[0023] The terms "first," "second," etc., used in the embodiments of this invention are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a technical feature defined with "first" or "second" may explicitly or implicitly include at least one of that feature.

[0024] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0025] This invention provides a model-aided calibration estimation method, apparatus, electronic device, and medium, which are described below.

[0026] Figure 1 This is a schematic flowchart of an embodiment of the model-assisted calibration estimation method provided by the present invention, as shown below. Figure 1 As shown, the model-aided calibration estimation method includes: S101. Extract non-probability samples from the target population and establish a multiple linear regression model between the research variables and covariates of the non-probability samples. Non-probability samples are drawn from the target population, and a multiple linear regression model is established between the research variable and covariates to analyze the relationship between the variables.

[0027] S102. Estimate the model parameters in the multiple linear regression model to obtain the estimated model parameters, and then estimate the research variables based on the estimated model parameters. The parameters in the multiple linear regression model are estimated to obtain the estimated model parameters, and the estimated values ​​of the research variables are obtained based on these parameters.

[0028] S103. Obtain the diagonal matrix corresponding to the original weights of the sample units in the non-probability sample. The original weights are obtained based on the sampling probability of the sample units. The initial weights are derived from the inclusion probability of the sample units, reflecting the representativeness of the sample in the population. The purpose of this step is to provide initial weights for subsequent calibration, ensuring that the original information of the sample is not lost.

[0029] S104. Obtain the Kullback-Leibler distance between the diagonal matrix and the preset calibration weights; Obtain the Kullback-Leibler distance between the diagonal matrix and the preset calibration weights to measure the difference between the two.

[0030] S105. Construct calibration constraints for target calibration weights based on the estimation of research variables; Based on the estimates of the research variables, calibration constraints can be constructed to ensure that the calibrated weights minimize the KL distance while satisfying these constraints. The purpose of this step is to incorporate domain knowledge (such as the estimates of the research variables) into the calibration process, thereby improving the relevance and accuracy of the calibration.

[0031] S106. Under calibration constraints, the calibration weights are calibrated to obtain the target calibration weights by minimizing the Kullback-Leibler distance; By optimizing the KL distance, the target calibration weights can be obtained, making the calibrated samples closer to the overall distribution. This step is the core of the calibration process, using optimization algorithms (such as gradient descent) to minimize the KL distance, thereby obtaining the optimal calibration weights.

[0032] S107. Estimation results of the overall mean of the target calibration weights based on the target calibration weights.

[0033] Based on the target calibrated weights, the population mean of the research variables can be estimated, improving the accuracy and reliability of the estimate. The purpose of this step is to use the calibrated weights to make a more accurate estimate of the population mean, thereby providing support for decision-making.

[0034] Compared with existing technologies, this embodiment provides a model-assisted calibration estimation method, including: extracting non-probability samples from the target population and establishing a multiple linear regression model between the research variables and covariates of the non-probability samples. The multiple linear regression model quantifies the linear relationship between the research variables and covariates, providing a basic model for subsequent calibration. The model parameters in the multiple linear regression model are estimated to obtain the estimated model parameters. Based on the estimated model parameters, the research variables are estimated. Through parameter estimation, the predicted values ​​of the research variables can be obtained, which are the basis for subsequent calibration weights. The diagonal matrix corresponding to the original weights of the sample units in the non-probability samples is obtained, with the original weights based on the sampling probability of the sample units. The Kullback-Leibler distance between the diagonal matrix and the preset calibration weights is obtained. By calculating the KL distance between the original weights and the preset calibration weights, the difference between the two can be quantified, providing an optimization target for subsequent calibration. The KL distance is chosen because it effectively measures the difference between two probability distributions, ensuring that the calibrated weights are closer to the preset calibration weights. Calibration constraints for the target calibration weights are constructed based on the estimation of the research variables. Under these constraints, the calibration weights are calibrated using the minimum Kullback-Leibler distance to obtain the target calibration weights. The estimated population mean of the target calibration weights is then determined based on these target calibration weights. This invention calibrates non-probability samples using a modified KL distance, significantly improving model calibration accuracy and generalization ability. It is particularly suitable for small sample or non-probability data scenarios, effectively mitigating the bias problem of traditional KL distance, making model predictions closer to the true distribution, and improving the calibration estimation effect for non-probability samples.

[0035] It should be noted that this invention is applied to non-probabilistic samples such as online surveys. For example, happiness index is selected as the research variable, and gender, age, education level, and annual family income are selected as covariates. In online survey satisfaction analysis, user satisfaction rating (1-10) is selected as the research variable, and gender, age, usage frequency, purchase intention, and product satisfaction are selected as covariates. In health survey risk assessment, disease risk index (0-1) is selected as the research variable, and age, gender, BMI, smoking history, and family medical history are selected as covariates. In education effectiveness evaluation, exam scores (0-100) are selected as the research variable, and gender, family economic status, study time, tutoring frequency, and teacher rating are selected as covariates. In market research purchase intention, purchase intention rating (0-10) is selected as the research variable, and gender, age, income level, brand preference, and advertising exposure frequency are selected as covariates. In sociological research on happiness surveys, happiness rating (0-10) is selected as the research variable, and marital status, job satisfaction, living environment, social support, and health status are selected as covariates.

[0036] These examples demonstrate the application of nonprobability sample calibration estimation in different fields, improving the accuracy and representativeness of research variable estimation by calibrating covariate weights. Understandably, this could also include nonprobability samples from other types of online surveys.

[0037] In a specific embodiment of the present invention, for the overall estimation of non-probability samples, a multiple linear regression model of the research variable and covariates is considered. SCAD is used for variable selection and model parameter estimation. Then, the non-probability samples are model-assistedly calibrated under the modified backward Kullback-Leibler distance, thereby estimating the population.

[0038] Specifically, in step S101, it is assumed that the non-probability sample... From the scale finite total In the sample drawn using a single-stage sampling method, the sample size is... Let the sample unit be... The probability of sample entry is , Sample unit and sample unit The joint sampling probability is , Sample unit The original weights are ; This represents a diagonal matrix representing the original weights.

[0039] The research variable is The covariates are , , Let be the number of covariates. The relationship between the variables and covariates is studied, following a superpopulation multiple linear regression model. In some embodiments of this invention, the expression of the multiple linear regression model is: ; ; ; In the formula, Indicates the research variable; Represent covariates; This represents the parameters of the multiple linear regression model. ; Indicates the error term , , .

[0040] When there are many covariates, selecting which covariates to build a super-population model becomes a problem. Different covariate choices will produce different super-population models, thus affecting the calibration effect and consequently the final population estimate. To improve the accuracy of the population estimate, the classic variable selection method SCAD is considered to select important covariates and estimate model parameters, and then calibration is performed based on this to estimate the population.

[0041] In some embodiments of the present invention, estimating the model parameters in the multiple linear regression model to obtain the estimated model parameters includes: The model parameters in the multiple linear regression model are estimated using the penalized regression algorithm, and the estimated model parameters are obtained.

[0042] In some embodiments of the present invention, in step S102, it is assumed that B is a parameter of the hyperpopulation model under a finite population. The estimate, If the estimate of B is a non-probability sample, then For the parameters of the super-population model The key to solving this problem is to find the estimate. The following section uses SCAD for variable selection and parameter estimation. Let... It is the penalty function of SCAD, namely: (1) in , and It is a parameter. Fan and Li have proven that in various cases, when The time parameter estimation has good properties. The basic idea of ​​SCAD is to study the sum of squared residuals of variables when the absolute values ​​of the coefficients conform to the penalty function (1). (2) Minimum, that is, the parameter estimation of the model based on SCAD is the parameter that minimizes Equation (2) under the condition of Equation (1). The Lagrange method is used to solve the problem. Let the Lagrange function be... The Lagrange parameter is ,but (3) Solving by Lagrange method Estimate for (4) In obtaining Estimates of the research variables can then be obtained. or .

[0043] In some embodiments of the present invention, the calibration constraints for constructing the target calibration weights based on the estimation of the research variables include: Obtain the constraints on the magnitude of the target calibration weights and the constraints on the estimation of the research variables; The size constraints and the estimated constraints of the studied variables are used as calibration constraints for the target calibration weights.

[0044] In some embodiments of the present invention, the step of calibrating the target calibration weights by minimizing the Kullback-Leibler distance under calibration constraints includes: The target calibration weights are obtained by calibrating the calibration weights with the minimum Kullback-Leibler distance under calibration constraints using the Lagrange method.

[0045] In a specific embodiment of the present invention, steps S104 to S106 are as follows: Based on the superpopulation model, further calibration is performed on the non-probability samples. Calibration weights are considered. Compared with the original weights The corrected backward Kullback-Leibler distance is (5) (6) (7) generally Thus, the calibration weights are the solutions that minimize equation (5) under the conditions of equations (6) and (7), where in equation (7) Equation (4) is given.

[0046] The calibration weights are solved using the Lagrange method, and the Lagrange function is given by... The Lagrange parameter is .definition , ,in Then the constraints of equations (3) and (4) can be expressed as follows: Further Lagrangian functions It can be written as: (17) Solving for the calibration weights yields the following: ,in , . The solution can be obtained using Newton's iteration method, thus... It can be written as (8) Its matrix form is expressed as ,in , (9) Let the function According to Taylor's formula, it can be written as (10) in , ,but (11) when From time to time Therefore, (12) thereby Can be written as (13) in Further Substitution Solve get (14) Therefore, the calibration weights can be written as (15) Since S is a non-probability sample, its initial weights The exact answer is unknown; however, Chen et al. (2018) have demonstrated that setting the initial weights of non-probability samples to the same sampling design (initial) weights as simple random samples still yields good estimation results. Therefore, consider setting the initial weights of non-probability samples to... , .

[0047] In a specific embodiment of the present invention, step S107 specifically includes the following steps: After obtaining the calibration weights based on the SCAD super-total model Subsequently, a total population estimate based on SCAD super-population model-assisted calibration can be obtained. for: (16) Or (17)

[0048] in = , The calibration slope that satisfies the calibration constraints is as follows: (18) in In some embodiments of the present invention, the expression for estimating the population mean is:

[0049] (19) In the formula, This represents an estimate of the population mean. Let represent the total number of units in the target population, i represent the i-th sample unit, and S represent the non-probability sample. Indicates the research variable, The constraint function representing the covariates. Represents the Lagrange parameters. Indicates the overall target. This represents the initial weight of sample unit i. This represents the model parameters obtained from the penalized regression algorithm.

[0050] To better illustrate the effectiveness of the method in this embodiment, specific examples are provided below.

[0051] Generate population Let the overall size be In this simulation, Let the finite population be a given population. The covariates are , It is the dimension of the covariates, taking... Let the first... Covariates With the Covariates The correlation coefficient is ,in It is a constant and ,Pick ,but The covariance matrix of the covariances is:

[0052] Let the model parameters be In this simulation, the following settings are provided.

[0053] Suppose the research variables are generated by the following linear model.

[0054] in .

[0055] Generate samples Poisson sampling was used to draw sample sizes from the population. The samples are non-probability samples of 500, 600, and 700. Let the unit... The probability of sample entry is , Generated from the following Logistic regression model:

[0056] Further revisions are needed. :

[0057] The final corrected sampling probability is: Poisson sampling is used to draw non-probability samples. Since the sample size drawn by Poisson sampling is generally random and non-fixed, in order to facilitate control of the sample size, [the following is used:] ... Adjustments were made to obtain Therefore, the adjusted Poisson sampling with a fixed probability of inclusion can draw a sample of essentially fixed size.

[0058] Estimate population mean After generating non-probability samples, the population mean was estimated using a model-aided calibration estimation method based on SCAD. For comparison, both the traditional calibration estimation method (Deville & Särndel, 1992) and the model-aided calibration estimation method were used simultaneously on the non-probability samples to obtain population mean estimates. The simulation was repeated 1000 times. On 1000 Monte Carlo samples, the bias, variance, and root mean square error of the population mean estimates obtained using the traditional calibration estimation method, the model-aided calibration estimation method, and the SCAD-based model-aided calibration estimation method were calculated respectively to evaluate the estimation performance of each method under the corrected backward Kullback-Leibler distance.

[0059] Simulation results The calculated bias, variance, and root mean square error of each estimate are shown in Table 1 for sample sizes of 500, 600, and 700. A plot of the root mean square error of the population mean estimate for different sample sizes is also shown. Figure 2 In this context, "GREG" represents the traditional calibration estimation method, "MC" represents the model-aided calibration estimation method, and "MCSCAD" represents the SCAD-based model-aided calibration estimation method.

[0060] Table 1: Simulation Results

[0061] As shown in Table 1, under different sample sizes, the absolute bias, variance, and root mean square error of the SCAD-based model-assisted calibration population mean estimation are relatively small, and all are smaller than those of the traditional calibration population mean estimation and the model-assisted calibration population mean estimation. This indicates that the SCAD-based model-assisted calibration population mean estimation has a relatively high degree of unbiasedness, almost unbiased, and its estimation efficiency is higher than that of the traditional calibration population mean estimation and the model-assisted calibration population mean estimation, showing the best estimation effect. Furthermore, Table 1 and... Figure 2 It is evident that as the sample size increases, the absolute bias, variance, mean square error, and root mean square error of the population mean estimation by the three methods all decrease.

[0062] In addition, to further illustrate the effectiveness of the method in this embodiment, data from the 2015 Internet user social awareness survey (http: / / www.cnsda.org / index.php?r=projects / view&id) were used. The figure =70846128 is used to illustrate this. The research method involves obtaining survey data from Chinese internet users through an online questionnaire, which is then used as the survey sample. This sampling survey is a non-probability sampling survey, and the obtained sample is a non-probability sample.

[0063] Data processing The happiness index was selected as the research variable, and set as follows: We selected four variables—gender, age, education level, and annual family income—as covariates, and set them as follows: According to different levels of happiness, Take values ​​respectively ;gender Select 1 and 2 for males and females respectively; age Please fill in the respondent's actual age; education level. Values ​​are assigned based on the highest level of education received; income The information should be filled in according to the respondents' annual income. Some variables and their meanings, along with their corresponding values, are shown in Table 2: Table 2 Variable Description

[0064] The original survey of netizens' social awareness contained 3781 cases. Because some respondents answered "I don't know," these cases were removed, leaving 3695 cases remaining. (Individual cases)

[0065] Estimation methods Based on data from a survey of internet users' social awareness, this study estimates the happiness index of Chinese residents using a SCAD-based model-assisted calibration estimation method, a traditional calibration estimation method, and a model-assisted calibration estimation method. The calibration weights obtained using the SCAD-based model-assisted calibration estimation method are: The estimated happiness index of residents is The calibration weights obtained using the traditional calibration estimation method are: The estimated happiness index of residents is The calibration weights obtained using the model-assisted calibration estimation method are: The estimated happiness index of residents is The three population means are estimated as follows: , ,

[0066] To compare the estimation performance of the three estimates, the bootstrap variances of each estimate are calculated. The basic idea for calculating the bootstrap variance is to repeatedly draw B subsamples from the original data, calculate B population mean estimates based on these B subsamples, and then calculate the variance of these B population mean estimates. Here, 100 (B=100) subsamples are repeatedly drawn from the actual data, and the above three estimation methods are used to calculate 100 estimates of the residents' happiness index. The variance of these 100 estimates is then calculated. By comparing the variance estimates of each estimate, the smaller the variance, the better the estimation performance.

[0067] Estimation results The happiness index and its variance estimates of residents were obtained using the SCAD-based model-assisted calibration estimation method, the traditional calibration estimation method, and the model-assisted calibration estimation method, as shown in Table 3. Table 3: Estimated Happiness Index and its Variance by Different Methods

[0068] As shown in Table 3, the happiness index obtained using the SCAD-based model-assisted calibration estimation method is 3.82022, indicating that residents generally consider themselves relatively happy. The happiness index obtained using the traditional calibration method and the model-assisted calibration estimation method is not significantly different from that obtained using the SCAD-based model-assisted calibration estimation method. The variance estimate obtained by the SCAD-based model-assisted calibration estimation method is smaller than that obtained by the other two estimation methods, indicating that the SCAD-based model-assisted calibration estimation method performs better than the traditional calibration method and the model-assisted calibration estimation method.

[0069] In summary, this embodiment presents a model-assisted calibration estimation method for estimating non-probability samples. First, the SCAD method is used to estimate the model parameters. Then, the calibration weights are calculated using the model-assisted calibration estimation method with a modified backward Kullback-Leibler distance, thereby estimating the total population and population mean of the non-probability samples. In the simulation analysis, the population mean of the non-probability samples was estimated using the traditional calibration estimation method, the model-assisted calibration estimation method, and the SCAD-based model-assisted calibration estimation method under different sample sizes. The bias, variance, and root mean square error of different estimates were calculated. The results show that, under different sample sizes, the SCAD-based model-assisted calibration estimation method outperforms the traditional calibration estimation method and the model-assisted calibration estimation method. In the empirical study, the model-assisted calibration estimation method based on SCAD was applied to the 2015 China Internet Users' Social Consciousness Survey data to obtain an estimate of the Chinese residents' happiness index. This embodiment proposes a model-assisted calibration estimation method when assuming a linear relationship between the research variables and covariates. When the relationship between the research variables and covariates is nonlinear, nonlinear parametric models, semi-parametric models and nonparametric models can be established, and the model-assisted calibration estimation method can be further explored.

[0070] To better implement the model-aided calibration estimation method in this embodiment of the invention, based on a model-aided calibration estimation method, correspondingly, as follows: Figure 3 As shown, this embodiment of the invention also provides a model-aided calibration estimation device. A model-aided calibration estimation device 300 includes: The multiple linear regression model building module 301 is used to extract non-probability samples from the target population and establish a multiple linear regression model between the research variables and covariates of the non-probability samples. The estimation module 302 for research variables is used to estimate the model parameters in the multiple linear regression model, obtain the estimated model parameters, and obtain the estimate of the research variables based on the estimated model parameters. The diagonal matrix acquisition module 303 is used to acquire the diagonal matrix corresponding to the original weights of the sample units in the non-probability sample. The original weights are obtained based on the sampling probability of the sample units. The distance acquisition module 304 is used to acquire the Kullback-Leibler distance between the diagonal matrix and the preset calibration weights; The constraint determination module 305 is used to construct calibration constraints for the target calibration weights based on the estimation of the research variables. The target calibration weight determination module 306 is used to calibrate the calibration weights to the minimum of the Kullback-Leibler distance under calibration constraints to obtain the target calibration weights; The overall mean estimation module 307 is used to determine the overall mean estimation result of the target calibration weights based on the target calibration weights.

[0071] The model-assisted calibration estimation device 300 provided in the above embodiments can realize the technical solution described in the above embodiment of the model-assisted calibration estimation method. The specific implementation principle of each module or unit can be found in the corresponding content in the above embodiment of the model-assisted calibration estimation method, which will not be repeated here.

[0072] like Figure 4 As shown, the present invention also provides an electronic device 400. The electronic device 400 includes a processor 401, a memory 402, and a display 403. Figure 4 Only some components of the electronic device 400 are shown, but it should be understood that it is not required to implement all the components shown, and more or fewer components may be implemented instead.

[0073] In some embodiments, processor 401 may be a central processing unit (CPU), microprocessor, or other data processing chip, used to run program code stored in memory 402 or process data, such as a model-aided calibration estimation method in this invention.

[0074] In some embodiments, processor 401 may be a single server or a group of servers. The server group may be centralized or distributed. In some embodiments, processor 401 may be local or remote. In some embodiments, processor 401 may be implemented on a cloud platform. In some embodiments, the cloud platform may include a private cloud, public cloud, hybrid cloud, community cloud, distributed cloud, internal cloud, multi-cloud, or any combination thereof.

[0075] In some embodiments, memory 402 may be an internal storage unit of electronic device 400, such as a hard disk or memory of electronic device 400. In other embodiments, memory 402 may also be an external storage device of electronic device 400, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. equipped on electronic device 400.

[0076] Furthermore, the memory 402 may include both internal storage units of the electronic device 400 and external storage devices. The memory 402 is used to store application software and various types of data installed on the electronic device 400.

[0077] In some embodiments, display 403 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, or an OLED (Organic Light-Emitting Diode) touchscreen. Display 403 is used to display information from electronic device 400 and to display a visual user interface. Components 401-403 of electronic device 400 communicate with each other via a system bus.

[0078] In one embodiment, when processor 401 executes a model-aided calibration estimation program in memory 402, the following steps can be implemented: Non-probability samples are extracted from the target population, and a multiple linear regression model is established between the research variables and covariates of the non-probability samples. The model parameters in the multiple linear regression model are estimated to obtain the estimated model parameters, and the estimated research variables are obtained based on the estimated model parameters. Obtain the diagonal matrix corresponding to the original weights of the sample units in the non-probability sample. The original weights are obtained based on the sampling probability of the sample units. Obtain the Kullback-Leibler distance between the diagonal matrix and the preset calibration weights; The calibration constraints for the target calibration weights are constructed based on the estimation of the research variables. Under calibration constraints, the target calibration weights are obtained by calibrating the calibration weights with the minimum Kullback-Leibler distance. The estimated result of determining the overall mean of the target calibration weights based on the target calibration weights.

[0079] It should be understood that when the processor 401 executes a model-aided calibration estimation program in the memory 402, in addition to the functions mentioned above, it can also perform other functions, as detailed in the description of the corresponding method embodiments above.

[0080] Furthermore, the embodiments of the present invention do not specifically limit the type of electronic device 400 mentioned. Electronic device 400 can be a mobile phone, tablet computer, personal digital assistant (PDA), wearable device, laptop computer, or other portable electronic device. Exemplary embodiments of portable electronic devices include, but are not limited to, portable electronic devices running iOS, Android, Microsoft, or other operating systems. The aforementioned portable electronic device can also be other portable electronic devices, such as a laptop computer with a touch-sensitive surface (e.g., a touch panel). It should also be understood that in some other embodiments of the present invention, electronic device 400 may not be a portable electronic device, but rather a desktop computer with a touch-sensitive surface (e.g., a touch panel).

[0081] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0082] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A model-aided calibration estimation method, characterized in that, include: Non-probability samples are extracted from the target population, and a multiple linear regression model is established between the research variables and covariates of the non-probability samples. The model parameters in the multiple linear regression model are estimated to obtain the estimated model parameters, and the estimated research variables are obtained based on the estimated model parameters. Obtain the diagonal matrix corresponding to the original weights of the sample units in the non-probability sample. The original weights are obtained based on the sampling probability of the sample units. Obtain the Kullback-Leibler distance between the diagonal matrix and the preset calibration weights; The calibration constraints for the target calibration weights are constructed based on the estimation of the research variables. Under calibration constraints, the target calibration weights are obtained by calibrating the calibration weights with the minimum Kullback-Leibler distance. The estimated result of determining the overall mean of the target calibration weights based on the target calibration weights.

2. The model-aided calibration estimation method according to claim 1, characterized in that, The expression for the multiple linear regression model is: In the formula, Indicates the research variable; Represent covariates; This represents the parameters of the multiple linear regression model. ; Indicates the error term , , .

3. The model-aided calibration estimation method according to claim 1, characterized in that, The estimation of model parameters in the multiple linear regression model, to obtain the estimated model parameters, includes: The model parameters in the multiple linear regression model are estimated using the penalized regression algorithm, and the estimated model parameters are obtained.

4. The model-aided calibration estimation method according to claim 3, characterized in that, The method of estimating the model parameters in the multiple linear regression model based on the penalized regression algorithm, to obtain the estimated model parameters, includes: Obtain the penalty function of the penalized regression algorithm, and the sum of squared covariances of the research variables; The Lagrange algorithm is used to find the target model parameters that minimize the sum of squared covariances of the research variables under the constraint of the penalty function. The target model parameters are estimated to obtain the estimated model parameters.

5. The model-aided calibration estimation method according to claim 1, characterized in that, The calibration constraints for constructing the target calibration weights based on the estimation of the research variables include: Obtain the constraints on the magnitude of the target calibration weights and the constraints on the estimation of the research variables; The size constraints and the estimated constraints of the studied variables are used as calibration constraints for the target calibration weights.

6. The model-aided calibration estimation method according to claim 1, characterized in that, The process of obtaining the target calibration weights by calibrating with the minimum Kullback-Leibler distance under calibration constraints includes: The target calibration weights are obtained by calibrating the calibration weights with the minimum Kullback-Leibler distance under calibration constraints using the Lagrange method.

7. The model-aided calibration estimation method according to claim 1, characterized in that, The expression for estimating the population mean is: In the formula, This represents an estimate of the population mean. Let represent the total number of units in the target population, i represent the i-th sample unit, and S represent the non-probability sample. Indicates the research variable, The constraint function representing the covariates. Represents the Lagrange parameters. Indicates the overall target. This represents the initial weight of sample unit i. This represents the model parameters obtained from the penalized regression algorithm.

8. A device for model-aided calibration estimation, characterized in that, include: The multiple linear regression model building module is used to extract non-probability samples from the target population and build a multiple linear regression model between the research variables and covariates of the non-probability samples. The module for estimating and obtaining research variables is used to estimate the model parameters in the multiple linear regression model, obtain the estimated model parameters, and then obtain the estimate of the research variables based on the estimated model parameters. The diagonal matrix acquisition module is used to obtain the diagonal matrix corresponding to the original weights of sample units in non-probability samples. The original weights are obtained based on the sampling probability of the sample units. The distance acquisition module is used to obtain the Kullback-Leibler distance between the diagonal matrix and the preset calibration weights; The constraint determination module is used to construct calibration constraints for the target calibration weights based on the estimation of the research variables. The target calibration weight determination module is used to calibrate the calibration weights to the minimum of the Kullback-Leibler distance under calibration constraints to obtain the target calibration weights; The overall mean estimation module is used to determine the overall mean of the target calibration weights based on the target calibration weights.

9. An electronic device, characterized in that, Including memory and processor, among which, The memory is used to store programs; The processor, coupled to the memory, is used to execute the program stored in the memory to implement the steps in the model-aided calibration estimation method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, Used to store computer-readable programs or instructions, which, when executed by a processor, can implement the steps in the model-aided calibration estimation method according to any one of claims 1 to 7.

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