Partially linear estimation using sufficient dimension reduction

Graduate School of Science and Engineering, Kagoshima University, Kagoshima 890-8580, Japan.
yoshida@sci.kagoshima-u.ac.jp

Received: 21 April 2015
Revised: 27 November 2015

Abstract

In this paper, we study estimation for partial linear models. We assume radial basis functions for the nonparametric component of these models. To obtain the estimated curve with fitness and smoothness of the nonparametric component, we first apply the sufficient dimension reduction method to the radial basis functions. Then, the coefficients of the transformed radial basis functions are estimated. Finally, the coefficients in the parametric component can be estimated. The above procedure is iterated and hence the proposed method is based on an alternating estimation. The proposed method is highly versatile and is applicable not only to mean regression but also quantile regression and general robust regression. The -consistency and asymptotic normality of the estimator are derived. A simulation study is performed and an application to a real dataset is illustrated.