Principal Components Regression Estimation in Semiparametric Partially Linear Additive Models

Abstract

Partially linear additive model is a popular multivariate nonparametric fitting technique. This paper considers estimation for the semiparametric model in the presence of multicollinearity. Combining the profile least-squares method and principal components regression technique, we propose a novel biased estimator for the regression coefficients, and provide the asymptotic bias and covariance matrix of the proposed estimator. A Monte Carlo simulation study is conducted to examine the performance of the proposed estimators and the results are satisfactory.