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

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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 10 scientific papers (total in 10 papers)

Short Communications

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

M. Bloznelis^a, H. Putter^b

^a The Faculty of Mathematics and Informatics, Vilnius University
^b Leiden University

Full-text PDF (864 kB) Citations (10)

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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\jour Theory Probab. Appl.

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Linking options:

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 10 articles:

Pascal Beckedorf, Angelika Rohde, “Non-uniform Bounds and Edgeworth Expansions in Self-normalized Limit Theorems”, J Theor Probab, 38:1 (2025)
Shakeeb Khan, Denis Nekipelov, “On uniform inference in nonlinear models with endogeneity”, Journal of Econometrics, 240:2 (2024), 105261
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
Qi-Man Shao, Qiying Wang, “Self-normalized limit theorems: A survey”, Probab. Surveys, 10:none (2013)
Wang Q., “Refined Self-normalized Large Deviations for Independent Random Variables”, J Theoret Probab, 24:2 (2011), 307–329
C&H/CRC Monographs on Statistics & Applied Probability, 20114852, Extreme Value Methods with Applications to Finance, 2011, 351
Jing B.-Y., Wang Q., “A Unified Approach to Edgeworth Expansions for a General Class of Statistics”, Stat Sin, 20:2 (2010), 613–636
Wang Qiying, Hall P., “Relative errors in central limit theorems for Student's $t$ statistic, with applications”, Statist. Sinica, 19:1 (2009), 343–354
S. Yu. Novak, “On self-normalized sums and Student's statistic”, Theory Probab. Appl., 49:2 (2005), 336–344
Hall P., Wang Qiying, “Exact convergence rate and leading term in central limit theorem for Student's $t$ statistic”, Ann. Probab., 32:2 (2004), 1419–1437

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Theory of Probability and its Applications

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