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Local Limit Theorem for the Supremum of an Empirical Process for I.I.D. Random Variables

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Abstract

In this paper, we establish the convergence in total-variation norm of the law of the supremum of an empirical process constructed from a sequence of i.i.d. random variables to the law of the supremum of a (generalized) Brownian bridge.

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Authors and Affiliations

  1. Laboratoire de Mathematiques et Applications, Universite de La Rochelle, Avenue Michel Cr'epeau, 17042, La Rochelle cedex, France

    J.-Ch. Breton

  2. Laboratoire de Mathematiques Paul Painleve, Universite Lille I, 59655, Villeneuve d'Acsq cedex, France

    Y. Davydov

Authors
  1. J.-Ch. Breton
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  2. Y. Davydov
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Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 457–478, October–December, 2005.

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Breton, JC., Davydov, Y. Local Limit Theorem for the Supremum of an Empirical Process for I.I.D. Random Variables. Lith Math J 45, 368–386 (2005). https://doi.org/10.1007/s10986-006-0002-6

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  • DOI: https://doi.org/10.1007/s10986-006-0002-6

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