Method for constructing missing sample probability density function estimator

A technique of probability density function and estimator, applied in nonlinear wavelet estimation, constructing the field of nonlinear wavelet estimator of probability density function of missing samples, which can solve the problem of inability to estimate non-smooth probability density function, so as to reduce deviation and improve effectiveness. Effect

Pending Publication Date: 2020-05-22
SHANGHAI MARITIME UNIVERSITY
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Problems solved by technology

[0005] Aiming at the deficiency that the existing missing data processing method cannot use the information of the missing data to construct the probability density function estimator, and the classic kernel estimation method

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  • Method for constructing missing sample probability density function estimator
  • Method for constructing missing sample probability density function estimator
  • Method for constructing missing sample probability density function estimator

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Embodiment Construction

[0053] With reference to accompanying drawing, further illustrate the present invention:

[0054] A method for constructing an estimator of a missing-sample probability density function comprising the steps of:

[0055] (1), using wavelet basis functions and wavelet coefficients to expand the real probability density function into wavelet form;

[0056] Suppose {X i ,1≤i≤n} is a d-dimensional covariate, Y i is affected by the covariate X i Affects the response variable, and has a probability density function f(y), for any f(y)∈L 2 (R) space can be expanded into the following wavelet form

[0057]

[0058] in, and beta kl =kl , f> is the wavelet coefficient, Form L 2 A set of orthonormal basis for (R) space. In order to study the convergence of the probability density function estimator, it is necessary to give k a truncation k 1 , so the probability density function can be expanded into the following form

[0059]

[0060] The probability density function f(...

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Abstract

The invention discloses a method for constructing a missing sample probability density function estimator. The method mainly comprises the following steps: (1) expanding a real probability density function by using a wavelet basis function; (2) constructing an unbiased estimator of a wavelet coefficient by using an inverse probability weighting method; (3) establishing a linear wavelet estimator of a probability density function by using a substitution estimation method; (4) selecting a hard threshold function to construct a probability density function nonlinear wavelet estimator; and (5) proving the optimal convergence rate of the nonlinear wavelet estimator, and finally, quantitatively analyzing the excellence of finite sample performance of the nonlinear wavelet estimator through analogue simulation. The method has the advantages that the discontinuous unknown function can be estimated, missing data is made up, the effectiveness of sample information is improved, and the estimatorconvergence speed is increased.

Description

technical field [0001] The invention relates to the technical field of missing sample construction, in particular to a method for constructing a nonlinear wavelet estimator of a probability density function of missing samples, and mainly relates to an inverse probability weighted missing data compensation method and a nonlinear wavelet estimation method. Background technique [0002] In engineering, every experiment will generate a large amount of data, and fully mining the information hidden in these data is of great significance for diagnosing faults, detecting signals, and improving work efficiency. In order to analyze the development law of phenomena that people care about and grasp the development process of the situation, the common method is to construct the probability density function of variables or processes. However, in practical applications, the probability density functions of the variables are unknown and need to be estimated. Commonly used estimation method...

Claims

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Application Information

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IPC IPC(8): G06F17/18
CPCG06F17/18
Inventor 邹玉叶顾邦平
Owner SHANGHAI MARITIME UNIVERSITY
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