Edgeworth expansion for U-statistics under minimal conditions

Bing Yi Jing; Qiying Wang

doi:10.1214/aos/1059655916

Edgeworth expansion for U-statistics under minimal conditions

Bing Yi Jing^*, Qiying Wang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

Berry-Esseen bounds for U-statistics under the optimal moment conditions were derived by Koroljuk and Borovskich and Friedrich. Under the same optimal moment assumptions with an additional nonlattice condition, we establish a one-term Edgeworth expansion with remainder o(n^-1/2) for U-statistics.

Original language	English
Pages (from-to)	1376-1391
Number of pages	16
Journal	Annals of Statistics
Volume	31
Issue number	4
DOIs	https://doi.org/10.1214/aos/1059655916
Publication status	Published - 1 Aug 2003

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title = "Edgeworth expansion for U-statistics under minimal conditions",

abstract = "Berry-Esseen bounds for U-statistics under the optimal moment conditions were derived by Koroljuk and Borovskich and Friedrich. Under the same optimal moment assumptions with an additional nonlattice condition, we establish a one-term Edgeworth expansion with remainder o(n-1/2) for U-statistics.",

keywords = "Edgeworth expansion, Nonlattice condition., Optimal moments, U-statistics",

author = "Jing, {Bing Yi} and Qiying Wang",

year = "2003",

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doi = "10.1214/aos/1059655916",

language = "English",

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T1 - Edgeworth expansion for U-statistics under minimal conditions

AU - Jing, Bing Yi

AU - Wang, Qiying

PY - 2003/8/1

Y1 - 2003/8/1

N2 - Berry-Esseen bounds for U-statistics under the optimal moment conditions were derived by Koroljuk and Borovskich and Friedrich. Under the same optimal moment assumptions with an additional nonlattice condition, we establish a one-term Edgeworth expansion with remainder o(n-1/2) for U-statistics.

AB - Berry-Esseen bounds for U-statistics under the optimal moment conditions were derived by Koroljuk and Borovskich and Friedrich. Under the same optimal moment assumptions with an additional nonlattice condition, we establish a one-term Edgeworth expansion with remainder o(n-1/2) for U-statistics.

KW - Edgeworth expansion

KW - Nonlattice condition.

KW - Optimal moments

KW - U-statistics

UR - http://www.scopus.com/inward/record.url?scp=0041857888&partnerID=8YFLogxK

U2 - 10.1214/aos/1059655916

DO - 10.1214/aos/1059655916

M3 - Article

SN - 0090-5364

VL - 31

SP - 1376

EP - 1391

JO - Annals of Statistics

JF - Annals of Statistics

IS - 4

ER -

Edgeworth expansion for U-statistics under minimal conditions

Abstract

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