Variance Estimation For Varying Index Coefficient Models With High-dimensional Data

The research of high dimensional data is the hotspot of statistical theory and applied research.In the case of high dimensional data,that is,the dimension of the variable is greater or greater than the sample size,so-called "curse of dimension ".At this point,the data is sparse and there is a pseudo-correlation between variables.The traditional error variance estimation technique,such as the na?ve two-stage method based on the least squares method,is undesirable and will seriously underestimate the level of variance of the model' error.The refitted cross-validation(RCV)improves the traditional na?ve two-stage method,and shows the accuracy and stability in variance estimation and variable selection.In order to avoid the curse of dimension,the semi-parametric regression model can solve the problem.The semi-parametric regression model also has the advantages of non-parametric regression model which is highly adaptable and advantages of parametric regression model which has strong release.This paper focuses on the refitted cross-validation method and semi-parametric regression model of varying index coefficient model(VICM).The parameter partial of the varying index coefficient models is estimated by the profile least squares method and the unknown function part is expanded by B-spline.Under the assumptions of high dimensional data,combine both of them.Simulation study and empirical analysis of the results show that the refitted cross-validation method is more accuracy and stability than traditional naive least squares for the general linear regression and the varying index coefficient model.