Solution of the Ill-Posed Semiparametric Regression Model Based on Singular Value Modification Restriction

Abstract EN

We propose a solution of the ill-posed semi-parametric regression model based on singular value modification restriction, aimed at the ill-posed problem of the normal matrix which may occur in the process of solving the semiparametric regression model.

First, the coefficient matrix is decomposed into singular values, and the smaller singular values are selected according to the criterion ∑i=1r1/σi/∑i=1n1/σi≤5% (in the singular value matrix, σ1>σ1>⋯>σr>⋯σn).

Second, the relatively smaller singular values are modified by the biased parameter to suppress the magnification of the estimated variance so as to effectively reduce the variance of parameter estimation, reduce the introduction of deviation and obtain more reliable parameter estimation.

The results of the numerical experiments show that the improved singular value modification restriction method can not only overcome the effect of the ill-posed normal matrix on the parameter estimation solution but also correctly separate the systematic errors and improve the accuracy of semiparametric regression model calculation results.