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Uniform Confidence Bands for Local Polynomial Quantile Estimators

Published online by Cambridge University Press:  25 July 2014

Camille Sabbah*
Affiliation:
Laboratoire EQUIPPE, Université Lille Nord de France, Domaine Universitaire du Pont de Bois, BP 60149, 59653 Villeneuve-d’Ascq Cedex, France. [email protected]
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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].

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2014

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