Journal of Probability and Statistics
Volume 2012 (2012), Article ID 138450, 18 pages
Research Article

New Bandwidth Selection for Kernel Quantile Estimators

Department of Mathematical Sciences, Brunel University, Uxbridge UBB 3PH, UK

Received 8 August 2011; Revised 26 September 2011; Accepted 10 October 2011

Academic Editor: Junbin B. Gao

Copyright © 2012 Ali Al-Kenani and Keming Yu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose a cross-validation method suitable for smoothing of kernel quantile estimators. In particular, our proposed method selects the bandwidth parameter, which is known to play a crucial role in kernel smoothing, based on unbiased estimation of a mean integrated squared error curve of which the minimising value determines an optimal bandwidth. This method is shown to lead to asymptotically optimal bandwidth choice and we also provide some general theory on the performance of optimal, data-based methods of bandwidth choice. The numerical performances of the proposed methods are compared in simulations, and the new bandwidth selection is demonstrated to work very well.