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UNIFORM BIAS STUDY AND BAHADURREPRESENTATION FOR LOCAL POLYNOMIAL ESTIMATORS OFTHE CONDITIONAL QUANTILE FUNCTION

Published online by Cambridge University Press:  02 August 2011

Emmanuel Guerre  and
Camille Sabbah
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Abstract

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This paper investigates the bias and the weak Bahadurrepresentation of a local polynomial estimator ofthe conditional quantile function and itsderivatives. The bias and Bahadur remainder term arestudied uniformly with respect to the quantilelevel, the covariates, and the smoothing parameter.The order of the local polynomial estimator can behigher than the differentiability order of theconditional quantile function. Applications of theresults deal with global optimal consistency ratesof the local polynomial quantile estimator,performance of random bandwidths, and estimation ofthe conditional quantile density function. Thelatter allows us to obtain a simple estimator of theconditional quantile function of the private valuesin a first-price sealed bids auction under theindependent private values paradigm and riskneutrality.

Information

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

Footnotes

This paper was started and completed when bothauthors were at Laboratoire de StatistiqueThéorique et Appliquée, Université Pierre et MarieCurie, support from which is gratefullyacknowledged. Financial support from theDepartment of Economics, Queen Mary University ofLondon, is also gratefully acknowledged. Theauthors thank the participants of the Queen MaryEconometrics Reading Group, of the Berlin QuantileRegression Workshop, and of the LSE Econometricsand Statistics Workshop in addition to theassociate editor and two anonymous referees whosecareful reading, suggestions, and comments helpedto improve the paper. All remaining errors are ourresponsibility.

References

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