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Teor. Veroyatnost. i Primenen., 2002, Volume 47, Issue 3, Pages 518–532 (Mi tvp3690)  

This article is cited in 7 scientific papers (total in 7 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 $S_n/V_n$, under symmetry conditions we consider Linnik-type zones, where the ratio $\mathbf{P}\{S_n/V_n\ge x\}/(1-\Phi(x))$ 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.

DOI: https://doi.org/10.4213/tvp3690

Full text: PDF file (1137 kB)

English version:
Theory of Probability and its Applications, 2003, 47:3, 415–428

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Received: 24.11.2001
Language:

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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\by G.~P.~Chistyakov, F.~G\"otze
\paper Moderate deviations for Student's statistic
\jour Teor. Veroyatnost. i Primenen.
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\pages 518--532
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\transl
\jour Theory Probab. Appl.
\yr 2003
\vol 47
\issue 3
\pages 415--428
\crossref{https://doi.org/10.1137/S0040585X97979846}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Theory Probab. Appl., 48:3 (2004), 528–535  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Wang Q.Y., “Limit theorems for self–normalized large deviation”, Electronic Journal of Probability, 10 (2005), 1260–1285  crossref  mathscinet  zmath  isi  scopus
    3. 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
    4. 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
    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. Wang Q., “Refined Self-normalized Large Deviations for Independent Random Variables”, J Theoret Probab, 24:2 (2011), 307–329  crossref  mathscinet  zmath  isi  scopus
    7. 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
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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