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Non-central limit theorems for random selections
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  • Published: 29 April 2009

Non-central limit theorems for random selections

  • István Berkes1,
  • Lajos Horváth2 &
  • Johannes Schauer1 

Probability Theory and Related Fields volume 147, pages 449–479 (2010)Cite this article

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  • 7 Citations

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Abstract

Selection from finite sets is a basic procedure of statistics and the partial sum behavior of selected elements is completely known under the “uniform asymptotic negligibility” condition of central limit theory. The purpose of the present paper is to determine the asymptotic behavior of partial sums when the central limit theorem fails. As an application, we describe the limiting properties of permutation and bootstrap statistics in case of infinite variance.

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Author information

Authors and Affiliations

  1. Institute of Statistics, Graz University of Technology, Münzgrabenstrasse 11, 8010, Graz, Austria

    István Berkes & Johannes Schauer

  2. Department of Mathematics, University of Utah, 155 South 1440 East, Salt Lake City, UT, 84112-0090, USA

    Lajos Horváth

Authors
  1. István Berkes
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  2. Lajos Horváth
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  3. Johannes Schauer
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Corresponding author

Correspondence to István Berkes.

Additional information

Dedicated to the memory of Sándor Csörgő.

I. Berkes’s research was supported by OTKA grants K 61052, K 67961, FWF grant S 9603-N23, and NSF-OTKA grant INT-0223262. L. Horváth’s research was supported by NSF grant DMS 0604670.

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Berkes, I., Horváth, L. & Schauer, J. Non-central limit theorems for random selections. Probab. Theory Relat. Fields 147, 449–479 (2010). https://doi.org/10.1007/s00440-009-0212-z

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  • Received: 07 May 2008

  • Revised: 20 November 2008

  • Published: 29 April 2009

  • Issue Date: July 2010

  • DOI: https://doi.org/10.1007/s00440-009-0212-z

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Keywords

  • Random selection
  • Uniform asymptotic negligibility
  • Bootstrap
  • Functional limit theorems
  • Permutation statistics

Mathematics Subject Classification (2000)

  • Primary 60F17
  • 62F40
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