Covariate-Adjusted Partially Linear Regression Models

Abstract

Abstract Motivated by covariate-adjusted regression (CAR) proposed by Sentürk and Müller (Citation2005) and an application problem, in this article we introduce and investigate a covariate-adjusted partially linear regression model (CAPLM), in which both response and predictor vector can only be observed after being distorted by some multiplicative factors, and an additional variable such as age or period is taken into account. Although our model seems to be a special case of covariate-adjusted varying coefficient model (CAVCM) given by Sentürk (Citation2006), the data types of CAPLM and CAVCM are basically different and then the methods for inferring the two models are different. In this article, the estimate method motivated by Cui et al. (Citation2008) is employed to infer the new model. Furthermore, under some mild conditions, the asymptotic normality of estimator for the parametric component is obtained. Combined with the consistent estimate of asymptotic covariance, we obtain confidence intervals for the regression coefficients. Also, some simulations and a real data analysis are made to illustrate the new model and methods. Keywords: Covariate-adjusted linear regressionNonparametric estimationPartially linear regressionMathematics Subject Classification: Primary 62F12Secondary 62F25, 62G05 Acknowledgments The second author was supported by NNSF project (10771123) of China, NBRP (973 Program 2007CB814901) of China, RFDP (20070422034) of China, NSF projects (Y2006A13 and Q2007A05) of Shandong Province of China.