Variable Selection For Partially Linear Varying Coefficient Models Under Complex Data

This article mainly studies variable selection for partially linear varying coefficient model.This model contains both linear model as parametric component and varying coefficient model as non-parametric function.Complex data such as missing data,measurement error data and longitudinal data are often encountered in theoretical research and practical data analysis.Variable selection can simultaneously choose significant variables to response from a large number of latent variables,and give an estimator for unknown parametric vector.Therefore,it has certain theoretical and practical significance to study the variable selection for partially linear varying coefficient model under complex data.The main research contents of this article are:(1)Variable selection for partially linear varying coefficient model with measurement errors in the non-parametric part and missing response under high-dimensional data is studied.Based on the local bias-corrected profile least-squares and the SCAD penalty function,two variable selection procedures are proposed by using complete case data and a semiparametric regression imputation technique.Under mild assumptions,the large sample properties such as consistency,sparsity and asymptotic normality of parametric estimators are established.The results of simulation experiments show the effectiveness of the proposed two variable selection methods,and imputation technique is superior to complete case data.(2)Variable selection for partially linear varying coefficient model with measurement errors in the non-parametric part under longitudinal data is studied.Based on B-spline function,approximating the varying coefficient function,the bias-corrected generalized estimation equation is established,and bias-corrected penalty quadratic inference function is constructed.Then,variable selection procedure is proposed.Under some assumptions,the asymptotic properties such as the consistency of the non-parametric estimator,the sparsity and the asymptotic normality of the parametric estimator are proved.The results of simulation experiments show that the proposed bias-corrected variable selection method is effective.