Covariate Selection for Linear Errors-in-Variables Regression Models

Abstract

Abstract In this article, we provide a procedure to select the significant covariates of the linear regression models in which some or all covariates are measured with errors. The proposed method is based on the combination of a non concave penalization and a corrected least squares, and it simultaneously selects significant covariates and estimates the unknown regression coefficients. Same as Fan and Li (Citation2001), we show the resulted estimator has an oracle property with a proper choice of regularization parameters and penalty function. Some simulation studies are conducted to illustrate the finite sample performance of the proposed method. Keywords: Linear regression modelMeasurement errorsNewton–Raphson algorithmNonconcave penalizationOracle propertyMathematics Subject Classification: Primary 62H12Secondary 62A10