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UNIFORM BIAS STUDY AND BAHADUR REPRESENTATION FOR LOCAL POLYNOMIAL ESTIMATORS OF THE CONDITIONAL QUANTILE FUNCTION

Published online by Cambridge University Press:  02 August 2011

Emmanuel Guerre  and
Camille Sabbah
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Abstract

This paper investigates the bias and the weak Bahadur representation of a local polynomial estimator of the conditional quantile function and its derivatives. The bias and Bahadur remainder term are studied uniformly with respect to the quantile level, the covariates, and the smoothing parameter. The order of the local polynomial estimator can be higher than the differentiability order of the conditional quantile function. Applications of the results deal with global optimal consistency rates of the local polynomial quantile estimator, performance of random bandwidths, and estimation of the conditional quantile density function. The latter allows us to obtain a simple estimator of the conditional quantile function of the private values in a first-price sealed bids auction under the independent private values paradigm and risk neutrality.

Type
Research Article
Information
Econometric Theory , Volume 28 , Issue 1 , February 2012 , pp. 87 - 129
Copyright
Copyright © Cambridge University Press 2011

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Footnotes

This paper was started and completed when both authors were at Laboratoire de Statistique Théorique et Appliquée, Université Pierre et Marie Curie, support from which is gratefully acknowledged. Financial support from the Department of Economics, Queen Mary University of London, is also gratefully acknowledged. The authors thank the participants of the Queen Mary Econometrics Reading Group, of the Berlin Quantile Regression Workshop, and of the LSE Econometrics and Statistics Workshop in addition to the associate editor and two anonymous referees whose careful reading, suggestions, and comments helped to improve the paper. All remaining errors are our responsibility.

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