Estimation And Variable Selection Of Two Kinds Of Semi-parametric Models Based On Mode Regression With Missing Data

In this paper,we mainly discuss the estimation and variable selection of partial linear additive models and partial linear single-index models based on the idea of the modal regression with missing data.The second chapter of this paper discusses the estimation and variable selection of models based on the concept of modal regression in the case of random missing response models for partial linear additivity models.Using the basis function of B-spline to approximate the non-parametric function part,combined with the modal regression and the Imputation-based penalty estimation method to give the penalty objective function under the missing data.The variable selection about the param-eter and non-parametric part are achieved by using of the double SCAD penalty function.Under certain conditions,the sparse nature and the Oracle property of the penalty estimate are proved,the validity and goodness of the method are tested by numerical simulation.The third chapter of this paper studies the estimation and variable selection of partial linear single-index models in view of the modal regression framework with missing data.The B-spline method is used to approximate the connect function of the single index part in the model.In the modal regression framework,the SCAD penalty function and the Imputation-based penalized estimation method are used to realize the selection of the important variables in the parameter part and the single index part of the model.Under certain conditions,the implementation steps of the penalty estimation algorithm are given by using of the MEM algorithm and the local quadratic approximation method,the theoretical properties of the penalty estimation are also proved.Finally,the robustness and validity of the proposed method are verified by numerical simulation.