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Moderate deviations in subsampling distribution estimation


Authors: Patrice Bertail, Anthony Gamst and Dimitris N. Politis
Journal: Proc. Amer. Math. Soc. 129 (2001), 551-557
MSC (1991): Primary 60F05; Secondary 60F10
Published electronically: July 27, 2000
MathSciNet review: 1707507
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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

DOI: https://doi.org/10.1090/S0002-9939-00-05551-9
Keywords: Central limit theorem, large deviations, resampling
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
Article copyright: © Copyright 2000 American Mathematical Society