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Journal of Probability and Statistics
Volume 2012, Article ID 834107, 33 pages
Research Article

General Bootstrap for Dual ϕ-Divergence Estimates

1Laboratoire de Mathématiques Appliquées, Université de Technologie de Compiègne, B.P. 529, 60205 Compiègne Cedex, France
2LSTA, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France

Received 30 May 2011; Revised 29 September 2011; Accepted 16 October 2011

Academic Editor: Rongling Wu

Copyright © 2012 Salim Bouzebda and Mohamed Cherfi. 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.


A general notion of bootstrapped ϕ-divergence estimates constructed by exchangeably weighting sample is introduced. Asymptotic properties of these generalized bootstrapped ϕ-divergence estimates are obtained, by means of the empirical process theory, which are applied to construct the bootstrap confidence set with asymptotically correct coverage probability. Some of practical problems are discussed, including, in particular, the choice of escort parameter, and several examples of divergences are investigated. Simulation results are provided to illustrate the finite sample performance of the proposed estimators.