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Teoriya Veroyatnostei i ee Primeneniya, 2002, Volume 47, Issue 2, Pages 374–381
DOI: https://doi.org/10.4213/tvp3669 (Mi tvp3669) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Short Communications

Second-order and bootstrap approximation to Student's $t$-statistic

M. Bloznelisa, H. Putterb

a The Faculty of Mathematics and Informatics, Vilnius University
b Leiden University
Full-text PDF (864 kB) Citations (9)
DOI: https://doi.org/10.4213/tvp3669
Abstract: We prove the validity of one-term Edgeworth expansion for Student's $t$-statistic under minimal conditions: the distribution of observations is nonlattice and has finite third moment. As a corollary we obtain the second-order correctness for the bootstrap of Student's t-statistic under these optimal conditions, thus extending classical result of Singh [Ann. Statist., 9 (1981), pp. 1187–1195] to the Studentized mean.
Keywords: Student test, Edgeworth expansion, bootstrap, asymptotic expansion, self-normalized sum.
Received: 13.05.1999
English version:
Theory of Probability and its Applications, 2003, Volume 47, Issue 2, Pages 300–307
DOI: https://doi.org/10.1137/S0040585X97979743
Bibliographic databases:
Document Type: Article
Language: English
Citation: M. Bloznelis, H. Putter, “Second-order and bootstrap approximation to Student's $t$-statistic”, Teor. Veroyatnost. i Primenen., 47:2 (2002), 374–381; Theory Probab. Appl., 47:2 (2003), 300–307
Citation in format AMSBIB
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\by M.~Bloznelis, H.~Putter
\paper Second-order and bootstrap approximation to Student's $t$-statistic
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\pages 374--381
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\zmath{https://zbmath.org/?q=an:1036.62007}
\transl
\jour Theory Probab. Appl.
\yr 2003
\vol 47
\issue 2
\pages 300--307
\crossref{https://doi.org/10.1137/S0040585X97979743}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000183800700009}
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  • https://www.mathnet.ru/eng/tvp3669
  • https://doi.org/10.4213/tvp3669
  • https://www.mathnet.ru/eng/tvp/v47/i2/p374
    • This publication is cited in the following 9 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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