Edgeworth approximations for distributions of symmetric statistics

Bloznelis M, Götze F (2022)
Probability Theory and Related Fields.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch
 
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Autor*in
Bloznelis, Mindaugas; Götze, FriedrichUniBi
Abstract / Bemerkung
We study the distribution of a general class of asymptotically linear statistics which are symmetric functions of N independent observations. The distribution functions of these statistics are approximated by an Edgeworth expansion with a remainder of order o(N-1). The Edgeworth expansion is based on Hoeffding's decomposition which provides a stochastic expansion into a linear part, a quadratic part as well as smaller higher order parts. The validity of this Edgeworth expansion is proved under Cramer's condition on the linear part, moment assumptions for all parts of the statistic and an optimal dimensionality requirement for the non linear part.
Stichworte
Edgeworth expansion; Littlewood-Offord problem; Concentration in lianach; spaces; Symmetric statistic; U-statistic; Hoeffding decomposition
Erscheinungsjahr
2022
Zeitschriftentitel
Probability Theory and Related Fields
ISSN
0178-8051
eISSN
1432-2064
Page URI
https://pub.uni-bielefeld.de/record/2964051

Zitieren

Bloznelis M, Götze F. Edgeworth approximations for distributions of symmetric statistics. Probability Theory and Related Fields. 2022.
Bloznelis, M., & Götze, F. (2022). Edgeworth approximations for distributions of symmetric statistics. Probability Theory and Related Fields. https://doi.org/10.1007/s00440-022-01144-x
Bloznelis, M., and Götze, F. (2022). Edgeworth approximations for distributions of symmetric statistics. Probability Theory and Related Fields.
Bloznelis, M., & Götze, F., 2022. Edgeworth approximations for distributions of symmetric statistics. Probability Theory and Related Fields.
M. Bloznelis and F. Götze, “Edgeworth approximations for distributions of symmetric statistics”, Probability Theory and Related Fields, 2022.
Bloznelis, M., Götze, F.: Edgeworth approximations for distributions of symmetric statistics. Probability Theory and Related Fields. (2022).
Bloznelis, Mindaugas, and Götze, Friedrich. “Edgeworth approximations for distributions of symmetric statistics”. Probability Theory and Related Fields (2022).

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