EFFICIENT SEMIPARAMETRIC ESTIMATION OF A PARTIALLY LINEAR QUANTILE REGRESSION MODEL

Abstract

This paper is concerned with estimating a conditional quantile function that is assumed to be partially linear. The paper develops a simple estimator of the parametric component of the conditional quantile. The semiparametric efficiency bound for the parametric component is derived, and two types of efficient estimators are considered. Asymptotic properties of the proposed estimators are established under regularity conditions. Some Monte Carlo experiments indicate that the proposed estimators perform well in small samples.This paper is a part of my Ph.D. dissertation submitted to the University of Iowa. I am grateful to my adviser, Joel Horowitz, for his insightful comments, suggestions, guidance, and support. I also thank John Geweke, Gene Savin, two anonymous referees, the co-editor Oliver Linton, and participants at the 2001 Midwest Econometrics Group Annual Meeting in Kansas City for many helpful comments and suggestions. Of course, the responsibility for any errors is mine.