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Two Stage Semi Parametric Quantile Regression

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  • J. M. Krief

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".

Suggested Citation

  • J. M. Krief, 2009. "Two Stage Semi Parametric Quantile Regression," Departmental Working Papers 2009-05, Department of Economics, Louisiana State University.
    • Handle: RePEc:lsu:lsuwpp:2009-05
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    References listed on IDEAS

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    3. Honore, Bo E & Hu, Luojia, 2004. "On the Performance of Some Robust Instrumental Variables Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 30-39, January.
    4. Severini, Thomas A. & Tripathi, Gautam, 2001. "A simplified approach to computing efficiency bounds in semiparametric models," Journal of Econometrics, Elsevier, vol. 102(1), pages 23-66, May.
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