Application Of ADMM Algorithm In High-Dimensional Partial Linear Measurement Error Model

This paper mainly studies the application of ADMM algorithm in parameter estima-tion arid variable selection of high-dimensional partial linear measurement error model.Unlike the classical partial linear model,the predictive variables in the model can not be directly observed,but the data with measurement errors can be observed.In this paper,we consider the case that he covariance of measurement error is known,more generally,the covariance of measurement error is unknown,and which can be estimated with observed data.For partial linear models,the general method is to estimate the non-linear part first,and then estimate the linear part by using the parameter estimation method.We use AD-MM algorithm to obtain the nearest neighbor matrix of the estimated covariance matrix,and use this matrix to estimate the parameters and select the variables.In this paper,we prove some theoretical properties of the penalty estimator obtained by this method under regular conditions.This paper is mainly composed of five parts:The first section briefly introduces the background of the partial linear model,general variable selection methods and the current.research results and the main problems in the measurement error model are discussed.In the second section,the adaptive Lasso estimator and the implementation algorithm of high-dimensional partial linear measurement error model are given.The third section in-vestigates the asymptotic properties of the proposed estimator.Simulation are conducted to asses the performance of the proposed method under small samples in the fourth section.The detailed proof of the theorems are relegated in the fifth section.