One-term Edgeworth expansion for finite population U-statistics of degree two

Bloznelis M, Götze F (1999)
ACTA APPLICANDAE MATHEMATICAE 58(1-3): 75-90.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Bloznelis, M; Götze, FriedrichUniBi
Abstract / Bemerkung
By means of Hoeffding's decomposition, we represent a finite population U-statistic of degree two by the sum of a linear and a quadratic part. Assuming that the linear part is nondegenerate, we prove the validity of one-term Edgeworth expansion for the distribution function of the statistic under the optimal (minimal) conditions on the linear part and 2 + delta moment condition on the quadratic part. No condition is imposed on the ratio N / n, where N, respectively n, denotes the sample size respectively the population size.
Stichworte
U-statistic; Edgeworth expansion; finite population
Erscheinungsjahr
1999
Zeitschriftentitel
ACTA APPLICANDAE MATHEMATICAE
Band
58
Ausgabe
1-3
Seite(n)
75-90
ISSN
0167-8019
Page URI
https://pub.uni-bielefeld.de/record/1621192

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Bloznelis M, Götze F. One-term Edgeworth expansion for finite population U-statistics of degree two. ACTA APPLICANDAE MATHEMATICAE. 1999;58(1-3):75-90.
Bloznelis, M., & Götze, F. (1999). One-term Edgeworth expansion for finite population U-statistics of degree two. ACTA APPLICANDAE MATHEMATICAE, 58(1-3), 75-90.
Bloznelis, M., and Götze, F. (1999). One-term Edgeworth expansion for finite population U-statistics of degree two. ACTA APPLICANDAE MATHEMATICAE 58, 75-90.
Bloznelis, M., & Götze, F., 1999. One-term Edgeworth expansion for finite population U-statistics of degree two. ACTA APPLICANDAE MATHEMATICAE, 58(1-3), p 75-90.
M. Bloznelis and F. Götze, “One-term Edgeworth expansion for finite population U-statistics of degree two”, ACTA APPLICANDAE MATHEMATICAE, vol. 58, 1999, pp. 75-90.
Bloznelis, M., Götze, F.: One-term Edgeworth expansion for finite population U-statistics of degree two. ACTA APPLICANDAE MATHEMATICAE. 58, 75-90 (1999).
Bloznelis, M, and Götze, Friedrich. “One-term Edgeworth expansion for finite population U-statistics of degree two”. ACTA APPLICANDAE MATHEMATICAE 58.1-3 (1999): 75-90.