A Berry-Esseen bound for student's statistic in the non-iid case

Bentkus V, Bloznelis M, Götze F (1996)
JOURNAL OF THEORETICAL PROBABILITY 9(3): 765-796.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Bentkus, V; Bloznelis, M; Götze, FriedrichUniBi
Abstract / Bemerkung
We establish a Berry-Esseen bound for Student's statistic for independent (nonidentically) distributed random variables. In particular, the bound implies a sharp estimate similar to the classical Berry-Esseen bound. In the i.i.d. case it yields sufficient conditions for the Central Limit Theorem for studentized sums. For non-i.i.d. random variables the bound shows that the Lindeberg condition is sufficient for the Central Limit Theorem for studentized sums.
Stichworte
non-identically distributed; random variables; convergence rate; Central Limit Theorem; self-normalized sums; Student's statistic; Berry-Esseen bound
Erscheinungsjahr
1996
Zeitschriftentitel
JOURNAL OF THEORETICAL PROBABILITY
Band
9
Ausgabe
3
Seite(n)
765-796
ISSN
0894-9840
Page URI
https://pub.uni-bielefeld.de/record/1638739

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Bentkus V, Bloznelis M, Götze F. A Berry-Esseen bound for student's statistic in the non-iid case. JOURNAL OF THEORETICAL PROBABILITY. 1996;9(3):765-796.
Bentkus, V., Bloznelis, M., & Götze, F. (1996). A Berry-Esseen bound for student's statistic in the non-iid case. JOURNAL OF THEORETICAL PROBABILITY, 9(3), 765-796.
Bentkus, V., Bloznelis, M., and Götze, F. (1996). A Berry-Esseen bound for student's statistic in the non-iid case. JOURNAL OF THEORETICAL PROBABILITY 9, 765-796.
Bentkus, V., Bloznelis, M., & Götze, F., 1996. A Berry-Esseen bound for student's statistic in the non-iid case. JOURNAL OF THEORETICAL PROBABILITY, 9(3), p 765-796.
V. Bentkus, M. Bloznelis, and F. Götze, “A Berry-Esseen bound for student's statistic in the non-iid case”, JOURNAL OF THEORETICAL PROBABILITY, vol. 9, 1996, pp. 765-796.
Bentkus, V., Bloznelis, M., Götze, F.: A Berry-Esseen bound for student's statistic in the non-iid case. JOURNAL OF THEORETICAL PROBABILITY. 9, 765-796 (1996).
Bentkus, V, Bloznelis, M, and Götze, Friedrich. “A Berry-Esseen bound for student's statistic in the non-iid case”. JOURNAL OF THEORETICAL PROBABILITY 9.3 (1996): 765-796.