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Teoriya Veroyatnostei i ee Primeneniya, 2003, Volume 48, Issue 3, Pages 609–615
DOI: https://doi.org/10.4213/tvp275 (Mi tvp275) 		 
This article is cited in 6 scientific papers (total in 6 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
Full-text PDF (886 kB) Citations (6)
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DOI: https://doi.org/10.4213/tvp275
Abstract: Let $X_1,X_2,\dots$ 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.
Received: 09.06.2003
English version:
Theory of Probability and its Applications, 2004, Volume 48, Issue 3, Pages 528–535
DOI: https://doi.org/10.1137/S0040585X97980610
Bibliographic databases:
Document Type: Article
Language: English
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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\jour Theory Probab. Appl.
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  • https://doi.org/10.4213/tvp275
  • https://www.mathnet.ru/eng/tvp/v48/i3/p609
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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