On minimal moment assumptions in Berry-Esseen theorems for U-statistics

Bentkus V, Götze F (1996)
THEORY OF PROBABILITY AND ITS APPLICATIONS 40(3): 430-445.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
The rate of convergence for asymptotically normal U-statistics is of order O(n(-1/2)) provided that E\E{h(X(1), X(2))/X(1)}\(3) < co and E\h(X(1), X(2))\(5/3) < co, where h is a symmetric kernel corresponding to the U-statistic. Bentkus, Gotze, and Zitikis [preprint 92-075, Universitat Bielefeld, 1992] have shown that the last moment condition is the best possible, that is, it cannot be replaced by a moment of order 5/3 - epsilon, for any epsilon > 0. In this paper we extend the result for statistics of higher orders and with possible nonnormal limit distributions.
Stichworte
convergence rate; U-statistics Berry-Esseen bound; lower bound
Erscheinungsjahr
1996
Zeitschriftentitel
THEORY OF PROBABILITY AND ITS APPLICATIONS
Band
40
Ausgabe
3
Seite(n)
430-445
ISSN
0040-585X
Page URI
https://pub.uni-bielefeld.de/record/1638303

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Bentkus V, Götze F. On minimal moment assumptions in Berry-Esseen theorems for U-statistics. THEORY OF PROBABILITY AND ITS APPLICATIONS. 1996;40(3):430-445.
Bentkus, V., & Götze, F. (1996). On minimal moment assumptions in Berry-Esseen theorems for U-statistics. THEORY OF PROBABILITY AND ITS APPLICATIONS, 40(3), 430-445. https://doi.org/10.1137/1140048
Bentkus, V., and Götze, F. (1996). On minimal moment assumptions in Berry-Esseen theorems for U-statistics. THEORY OF PROBABILITY AND ITS APPLICATIONS 40, 430-445.
Bentkus, V., & Götze, F., 1996. On minimal moment assumptions in Berry-Esseen theorems for U-statistics. THEORY OF PROBABILITY AND ITS APPLICATIONS, 40(3), p 430-445.
V. Bentkus and F. Götze, “On minimal moment assumptions in Berry-Esseen theorems for U-statistics”, THEORY OF PROBABILITY AND ITS APPLICATIONS, vol. 40, 1996, pp. 430-445.
Bentkus, V., Götze, F.: On minimal moment assumptions in Berry-Esseen theorems for U-statistics. THEORY OF PROBABILITY AND ITS APPLICATIONS. 40, 430-445 (1996).
Bentkus, V, and Götze, Friedrich. “On minimal moment assumptions in Berry-Esseen theorems for U-statistics”. THEORY OF PROBABILITY AND ITS APPLICATIONS 40.3 (1996): 430-445.

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