Model Detection And Variable Selection For Covariate-adjusted Varying-coefficient Models

In this paper,we focus on parameter estimations and function coefficient diagnosis of covariate-adjusted varying-coefficient models.The predictors and response variables in this model cannot be directly observed,but they can be observed after they are distort-ed.This paper firstly recovers the predictor variables and response variables that cannot be directly observed,and then use the combination of local polynomials,Group Lasso and SCAD penalty functions to achieve the purpose of simultaneously selecting variables and diagnosing constant coefficients and function coefficients,and prove the obtained penalty estimators have the Oracle property under regular conditions.That is,the parameter es-timators and function coefficient estimators have the same asymptotic expectations and variances as the estimators obtained when the non-zero coefficient sets are known.And this method can identify the varying-coefficient terms,non-zero constant terms,zero terms in the model with probability 1.This paper is mainly composed of five parts:The first part briefly introduces the proposed background of covariate-adjusted varying-coefficient models,general variable s-election methods and the current research results and the main research content of this paper.The second part gives the variable selection method and the specific calculation process of this model.The third part studies the asymptotic properties of the estimators obtained by the method proposed in this paper.The fourth part uses numerical simula-tion to verify the effectiveness of the method.The fifth part gives the regular constraint conditions and a detailed proof of the third part of the theorems.