Modal Regression And Variable Selection For Two Semiparametric Models

In this paper,based on modal regression,we mainly study the problem of variable selection for the partially linear additive models and semiparametric partially linear varying coefficient model with missing data.In the first part,we discuss estimation and variable selection procedure for the partially linear additive models based on modal regression.The nonparametric functions are approximated by B-spline basis.Then,we use adaptive least absolute shrinkage and selection operator(LASSO)penalty function to realize variable selection of parametric and nonparametric components simultaneously.Its large sample properties is also established.Under appropriate conditions,we can prove that the variable selection method has oracle property.Furthermore,we give the bandwidth selection method and apply EM-type algorithm to realize the proposed method.Finally,numerical simulation study is undertaken to show the effectiveness of the proposed variable selection procedure.The second purpose of this article is to discuss robust estimation and variable selection for semiparametric partially linear varying coefficient model based on modal regression with missing data.In the case of response missing at random,we use the idea of modal regression and combine with imputation-based penalized estimating to study the estimation of unknown parameters and coefficient functions.Moreover,apply SCAD penalty function to select significant variables in parametric and nonparametric components simultaneously.Under appropriate conditions,we establish its consistency for both parametric and nonparametric part,obtaining the sparse property of penalized estimators,and asymptotic distribution of the estimators for nonzero coefficients in the parametric components.Some simulations comparison are carried out to assess the effectiveness of the proposed methods.Finally,the theoretical and numerical simulation results of this paper can effectively illustrate the effectiveness of the variable selection method.