An Edgeworth expansion for symmetric statistics

Bentkus V, Götze F, van Zwet WR (1997)
ANNALS OF STATISTICS 25(2): 851-896.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor/in
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Abstract / Bemerkung
We consider asymptotically normal statistics which are symmetric functions of N i.i.d. random variables. For these statistics we prove the validity of an Edgeworth expansion with remainder O(N-1) under Cramer's condition on the linear part of the statistic and moment assumptions for all parts of the statistic. By means of a counterexample we show that it is generally not possible to obtain an Edgeworth expansion with remainder o(N-1) without imposing additional assumptions on the structure of the nonlinear part of the statistic.
Stichworte
Hoeffding's decomposition; U-statistics; functions of sample means; functionals of empirical distribution functions; linear combinations of; order statistics; asymptotic expansion; Student's statistic; Edgeworth expansions; symmetric statistics
Erscheinungsjahr
1997
Zeitschriftentitel
ANNALS OF STATISTICS
Band
25
Ausgabe
2
Seite(n)
851-896
ISSN
0090-5364
Page URI
https://pub.uni-bielefeld.de/record/1623340

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Bentkus V, Götze F, van Zwet WR. An Edgeworth expansion for symmetric statistics. ANNALS OF STATISTICS. 1997;25(2):851-896.
Bentkus, V., Götze, F., & van Zwet, W. R. (1997). An Edgeworth expansion for symmetric statistics. ANNALS OF STATISTICS, 25(2), 851-896.
Bentkus, V., Götze, F., and van Zwet, W. R. (1997). An Edgeworth expansion for symmetric statistics. ANNALS OF STATISTICS 25, 851-896.
Bentkus, V., Götze, F., & van Zwet, W.R., 1997. An Edgeworth expansion for symmetric statistics. ANNALS OF STATISTICS, 25(2), p 851-896.
V. Bentkus, F. Götze, and W.R. van Zwet, “An Edgeworth expansion for symmetric statistics”, ANNALS OF STATISTICS, vol. 25, 1997, pp. 851-896.
Bentkus, V., Götze, F., van Zwet, W.R.: An Edgeworth expansion for symmetric statistics. ANNALS OF STATISTICS. 25, 851-896 (1997).
Bentkus, V, Götze, Friedrich, and van Zwet, WR. “An Edgeworth expansion for symmetric statistics”. ANNALS OF STATISTICS 25.2 (1997): 851-896.