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Some results on the influence of extremes on the bootstrap

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Some results on the influence of extremes on the bootstrap ANNALES DE L’I. H. P., SECTION B PAUL DEHEUVELS DAVID M. MASON GALEN R. SHORACK Some results on the influence of extremes on the bootstrap Annales de l’I. H. P., section B, tome 29, no 1 (1993), p. 83-103. <http://www.numdam.org/item?id=AIHPB_1993__29_1_83_0> © Gauthier-Villars, 1993, tous droits réservés. L’accès aux archives de la revue « Annales de l’I. H. P., section B » (http://www.elsevier.com/locate/anihpb), implique l’accord avec les condi- tions générales d’utilisation (http://www.numdam.org/legal.php). Toute uti- lisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit conte- nir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ 83 Some results on the influence of extremes on the bootstrap Paul DEHEUVELS (*) L.S.T.A., Tour 45-55, E 3, Université Paris-VI, 4, place Jussieu, 75252 Paris Cedex 05 David M. MASON (**) Department of Mathematical, Sciences, 501 Ewing Hall, University of Delaware, Newark, DE 19716, U.S.A. Galen R. SHORACK Department of Statistics,GN-22, University of Washington, Seattle, WA 98195, U.S.A. Ann. Inst. Henri Poincaré, Vol. 29, n° 1, 1993, p. .103. Probabilités et Statistiques ABSTRACT. - We study the influence of the extremes in the construction of consistent bootstraps in three illustrative situations. These are bootstrap- ping maxima. bootstrapping intermediate trimmed means and bootstrap- ping means. In the process, we shed new light upon the problem of bootstrapping the mean and obtain refinements and improvements of previous results. We also expose some interesting asymptotic distributional curiosities in connection with this problem. Our approach throughout is novel, in the sense that we work purely within the quantile function uniform empirical process methodology. (*) Recherche fi

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