The Berry-Esseen bound for student's statistic

Bentkus V, Götze F (1996)
ANNALS OF PROBABILITY 24(1): 491-503.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We prove the Berry-Esseen bound for the Student t-statistic. Under the assumption of a third moment this bound coincides (up to an absolute constant) with the classical Berry-Esseen bound for the mean. In general the distribution of the Student statistic converges to the standard normal distribution function at least as fast as the distribution of the mean, and sometimes faster. For example, rates of convergence can be proved if the underlying distribution is in the domain of attraction of the normal law.
Stichworte
student's statistic; convergence rate; central; limit theorem; self-normalized; Berry-Esseen bound
Erscheinungsjahr
1996
Zeitschriftentitel
ANNALS OF PROBABILITY
Band
24
Ausgabe
1
Seite(n)
491-503
ISSN
0091-1798
Page URI
https://pub.uni-bielefeld.de/record/1638950

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Bentkus V, Götze F. The Berry-Esseen bound for student's statistic. ANNALS OF PROBABILITY. 1996;24(1):491-503.
Bentkus, V., & Götze, F. (1996). The Berry-Esseen bound for student's statistic. ANNALS OF PROBABILITY, 24(1), 491-503.
Bentkus, V., and Götze, F. (1996). The Berry-Esseen bound for student's statistic. ANNALS OF PROBABILITY 24, 491-503.
Bentkus, V., & Götze, F., 1996. The Berry-Esseen bound for student's statistic. ANNALS OF PROBABILITY, 24(1), p 491-503.
V. Bentkus and F. Götze, “The Berry-Esseen bound for student's statistic”, ANNALS OF PROBABILITY, vol. 24, 1996, pp. 491-503.
Bentkus, V., Götze, F.: The Berry-Esseen bound for student's statistic. ANNALS OF PROBABILITY. 24, 491-503 (1996).
Bentkus, V, and Götze, Friedrich. “The Berry-Esseen bound for student's statistic”. ANNALS OF PROBABILITY 24.1 (1996): 491-503.