Volume 18, 2014
|Page(s)||265 - 276|
|Published online||25 July 2014|
Uniform Confidence Bands for Local Polynomial Quantile Estimators∗
Laboratoire EQUIPPE, Université Lille Nord de France, Domaine Universitaire du Pont de Bois, BP 60149, 59653 Villeneuve-d’Ascq Cedex, France
Received: 3 March 2011
Revised: 14 June 2012
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].
Mathematics Subject Classification: 62G08 / 62G15
Key words: Uniform confidence bands / conditional quantile estimation
This paper was started when the author was at Laboratoire de Statistique Théorique et Appliquée, Université Pierre et Marie Curie, support from which is gratefully acknowledged. The author thank the associate editor and two anonymous referees whose careful reading, suggestions, and comments helped to improve the paper. We also would like to thank Professor Emmanuel Guerre for helpful comments and discussions. All remaining errors are our responsibility.
© EDP Sciences, SMAI, 2014
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