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Complete Convergence

  • Conference paper
Asymptotic Statistics

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

Abstract

The concept complete convergence was introduced in 1947 by Hsu and Robbins, who proved that the sequence of arithmetic means of i.i.d. random variables converges completely to the expected value of the variables provided their variance is finite. In this paper we summarize a number of extensions and generalizations of that result.

AMS 1980 subject classifications

Primary: 60F15, 60G50 Secondary: 60G40

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Author information

Authors and Affiliations

  1. Department of Mathematics, Uppsala University, Box 480, S-751 06, Uppsala, Sweden

    Allan Gut

Authors
  1. Allan Gut
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Editor information

Editors and Affiliations

  1. Department of Probability and Mathematical Statistics, Charles University, Sokolovská 83, CZ-186 00, Praha 8, Czech Republic

    Petr Mandl  & Marie Hušková  & 

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© 1994 Springer-Verlag Berlin Heidelberg

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Gut, A. (1994). Complete Convergence. In: Mandl, P., Hušková, M. (eds) Asymptotic Statistics. Contributions to Statistics. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57984-4_19

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  • DOI: https://doi.org/10.1007/978-3-642-57984-4_19

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-0770-7

  • Online ISBN: 978-3-642-57984-4

  • eBook Packages: Springer Book Archive

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