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Teor. Veroyatnost. i Primenen., 2003, Volume 48, Issue 3, Pages 609–615 (Mi tvp275)  

This article is cited in 4 scientific papers (total in 4 papers)

Short Communications

On bounds for moderate deviations for Student's statistic

G. P. Chistyakova, F. Götzeb

a B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine
b Bielefeld University

Abstract: Let $X_1,X_2,…$ be independent random variables with zero means and finite variances. In this paper we prove lower bounds for a Cramér-type large deviation theorem for self-normalized sums which imply that the bounds obtained by Jing, Shao, and Wang [Ann. Probab., 31 (2003), pp. 2167–2215] are sharp.

Keywords: Linnik zones, self-normalized sum, $t$-statistic, moderate deviations, nonuniform bounds.

DOI: https://doi.org/10.4213/tvp275

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English version:
Theory of Probability and its Applications, 2004, 48:3, 528–535

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Received: 09.06.2003
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Citation: G. P. Chistyakov, F. Götze, “On bounds for moderate deviations for Student's statistic”, Teor. Veroyatnost. i Primenen., 48:3 (2003), 609–615; Theory Probab. Appl., 48:3 (2004), 528–535

Citation in format AMSBIB
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\paper On bounds for moderate deviations for Student's statistic
\jour Teor. Veroyatnost. i Primenen.
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\transl
\jour Theory Probab. Appl.
\yr 2004
\vol 48
\issue 3
\pages 528--535
\crossref{https://doi.org/10.1137/S0040585X97980610}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Robinson J., Wang Qiying, “On the self-normalized Cramer-type large deviation”, J. Theoret. Probab., 18:4 (2005), 891–909  crossref  mathscinet  zmath  isi  scopus
    2. Dembo A., Shao Qi-Man, “Large and moderate deviations for Hotelling's $T^2$-statistic”, Electron. Comm. Probab., 11 (2006), 149–159  crossref  mathscinet  zmath  isi  scopus
    3. Wang Q., “Refined Self-normalized Large Deviations for Independent Random Variables”, J Theoret Probab, 24:2 (2011), 307–329  crossref  mathscinet  zmath  isi  scopus
    4. Shao Q.-m. Zhou W.-x., “Self-Normalization: Taming a Wild Population in a Heavy-Tailed World”, Appl. Math.-J. Chin. Univ. Ser. B, 32:3 (2017), 253–269  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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