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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Moderate deviations in subsampling distribution estimation
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by Patrice Bertail, Anthony Gamst and Dimitris N. Politis PDF
Proc. Amer. Math. Soc. 129 (2001), 551-557 Request permission

Abstract:

In Politis and Romano (1994) the subsampling methodology was put forth for approximating the sampling distribution (and the corresponding quantiles) of general statistics from i.i.d. and stationary data. In this note, we address the question of how well the subsampling distribution approximates the tail of the target distribution. In the regular setting of the sample mean of an $m$-dependent sequence we show a moderate deviation property of the subsampling distribution.
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Additional Information
  • Patrice Bertail
  • Affiliation: INRA-CORELA, 65, Bd. de Brandebourg, 34205 Ivry-Seine, France
  • Anthony Gamst
  • Affiliation: Department of Mathematics, University of California at San Diego, La Jolla, California 92093-0112
  • Email: acgamst@osiris.ucsd.edu
  • Dimitris N. Politis
  • Affiliation: Department of Mathematics, University of California at San Diego, La Jolla, California 92093-0112
  • Email: politis@euclid.ucsd.edu
  • Received by editor(s): April 6, 1998
  • Received by editor(s) in revised form: April 30, 1999
  • Published electronically: July 27, 2000
  • Communicated by: Stanley Sawyer
  • © Copyright 2000 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 551-557
  • MSC (1991): Primary 60F05; Secondary 60F10
  • DOI: https://doi.org/10.1090/S0002-9939-00-05551-9
  • MathSciNet review: 1707507