Adaptive LASSO Estimation For Covariate Adjusted Partially Linear Regression Models

This paper studies the estimation of the high-dimensional Covariate Adjusted Partially Linear Regression Models and the variable selection problem.Covariate Adjusted Partially Linear Regression Model combines the good interpretability of the linear regression model with the flexibility of the nonparametric model.Different linear models,the response variables and predictors in this paper are not directly observable,but they are observable after some observable covariates are distorted.This paper estimates the adaptive LASSO parameters of some linear covariate adjustment models.The variable selection method is studied and it is proved that the penalty estimate of the parameter part has the Oracle property,that is,the method can accurately identify the non-zero coefficient and has the same variance as the estimate directly from the significant variable set.This estimation method is convenient for calculation.Finally,the small sample nature of the estimator was studied through simulation.The results show that the variable selection and parameter estimation works well.The paper's arrangement is as follows.In Chapter 1,the introduction of a covariate adjusted partial linear regression model(CAPLM),introduces the research background of the CAPLM model and the main work of this paper.In Chapter 2,we proposed CAPLM.The model's adaptive LASSO variable selection method,and constructed a new estimator,obtained the estimation of the parameter and non-parametric part.In Chapter 3,we studied the asymptotic properties of the estimator,and proved that the??? LASSO parameter estimation of the CAPLM model has Oracle property.finite samples is studied through simulation.In Chapter 5,the detailed samples is studied through simulation.In Chapter 5,the detailed theorem proving process is given.