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Uniform Confidence Bands for Local Polynomial Quantile Estimators∗

Published online by Cambridge University Press:  25 July 2014

Camille Sabbah
Camille Sabbah*
Affiliation:
Laboratoire EQUIPPE, Université Lille Nord de France, Domaine Universitaire du Pont de Bois, BP 60149, 59653 Villeneuve-d’Ascq Cedex, France. camille.sabbah@univ-lille3.fr
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Abstract

This paper deals with uniform consistency and uniform confidence bands for the quantile function and its derivatives. We describe a kernel local polynomial estimator of quantile function and give uniform consistency. Furthermore, we derive its maximal deviation limit distribution using an approximation in the spirit of Bickel and Rosenblatt [P.J. Bickel and M. Rosenblatt, Ann. Statist. 1 (1973) 1071–1095].

Keywords

Uniform confidence bandsconditional quantile estimation
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 18 , 2014 , pp. 265 - 276
Copyright
© EDP Sciences, SMAI, 2014

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