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Teoriya Veroyatnostei i ee Primeneniya, 2002, Volume 47, Issue 3, Pages 518–532
DOI: https://doi.org/10.4213/tvp3690
(Mi tvp3690)
 

This article is cited in 9 scientific papers (total in 9 papers)

Moderate deviations for Student's statistic

G. P. Chistyakova, F. Götzeb

a Institute for Low Temperature Physics and Engineering, Ukraine Academy of Sciences
b Bielefeld University, Department of Mathematics
Abstract: For self-normalized sums, say Sn/Vn, under symmetry conditions we consider Linnik-type zones, where the ratio P{Sn/Vnx}/(1Φ(x)) converges to 1, and establish optimal bounds for remainder terms related to this convergence.
Keywords: Linnik zones, self-normalized sum, t-statistic, moderate deviations, nonuniform bounds.
Received: 24.11.2001
English version:
Theory of Probability and its Applications, 2003, Volume 47, Issue 3, Pages 415–428
DOI: https://doi.org/10.1137/S0040585X97979846
Bibliographic databases:
Document Type: Article
Language: English
Citation: G. P. Chistyakov, F. Götze, “Moderate deviations for Student's statistic”, Teor. Veroyatnost. i Primenen., 47:3 (2002), 518–532; Theory Probab. Appl., 47:3 (2003), 415–428
Citation in format AMSBIB
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\paper Moderate deviations for Student's statistic
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\transl
\jour Theory Probab. Appl.
\yr 2003
\vol 47
\issue 3
\pages 415--428
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Linking options:
  • https://www.mathnet.ru/eng/tvp3690
  • https://doi.org/10.4213/tvp3690
  • https://www.mathnet.ru/eng/tvp/v47/i3/p518
  • This publication is cited in the following 9 articles:
    1. Pascal Beckedorf, Angelika Rohde, “Non-uniform Bounds and Edgeworth Expansions in Self-normalized Limit Theorems”, J Theor Probab, 38:1 (2025)  crossref
    2. Liu W. Shao Q.-M. Wang Q., “Self-Normalized Cramer Type Moderate Deviations for the Maximum of Sums”, Bernoulli, 19:3 (2013), 1006–1027  crossref  mathscinet  zmath  isi  scopus
    3. Qi-Man Shao, Qiying Wang, “Self-normalized limit theorems: A survey”, Probab. Surveys, 10:none (2013)  crossref
    4. Wang Q., “Refined Self-normalized Large Deviations for Independent Random Variables”, J Theoret Probab, 24:2 (2011), 307–329  crossref  mathscinet  zmath  isi  scopus
    5. Goldstein L., Shao Q.-M., “Berry–Esseen Bounds for Projections of Coordinate Symmetric Random Vectors”, Electronic Communications in Probability, 14 (2009), 474–485  crossref  mathscinet  zmath  isi  scopus
    6. Bertail P., Gautherat E., Harari-Kermadec H., “Exponential Bounds for Multivariate Self–Normalized Sums”, Electronic Communications in Probability, 13 (2008), 628–640  crossref  mathscinet  zmath  isi  scopus
    7. Wang Q.Y., “Limit theorems for self–normalized large deviation”, Electronic Journal of Probability, 10 (2005), 1260–1285  crossref  mathscinet  zmath  isi  scopus
    8. Robinson J., Wang Q.Y., “On the self–normalized Cramer–type large deviation”, Journal of Theoretical Probability, 18:4 (2005), 891–909  crossref  mathscinet  zmath  isi  scopus
    9. Theory Probab. Appl., 48:3 (2004), 528–535  mathnet  crossref  crossref  mathscinet  zmath  isi
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