Two Stage Semi Parametric Quantile Regression

J. M. Krief

Departmental Working Papers from Department of Economics, Louisiana State University

Abstract: We propose a root n consistent estimator for B0 when the qth conditional quantile of Y given X=x and Z=z takes the semi linear form g(x)+z'B0 where g(.) is an un- known real valued function,B0 a finite dimensional parameter and (X,Z) a couple of explanatory variables. Importantly, our estimator attains,under homoscedasticity,the semi parametric efficiency bound. This estimation is conducted in two steps. First, a Robinson's like demeaning of the original model is employed which provides a new quantile regression whose nuisance terms are estimated via a non parametric proce- dure.In the second stage, a quantile regression is conducted by smoothing the check function. We show that the previous estimator belongs to a class of estimators we propose to name "two stage semi parametric quantile".

Date: 2009-05
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