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The Berry‐Esseen bound for Studentized U ‐statistics
Author(s) -
Helmers R.
Publication year - 1985
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315169
Subject(s) - studentized range , mathematics , statistics , humanities , combinatorics , philosophy , standard error
Callaert and Veraverbeke (1981) recently obtained a Berry‐Esseen‐type bound of order n –1/2 for Studentized nondegenerate U ‐statistics of degree two. The condition these authors need to obtain this order bound is the finiteness of the 4.5th absolute moment of the kernel h . In this note it is shown that this assumption can be weakened to that of a finite (4 + ϵ)th absolute moment of the kernel h , for some ϵ > 0. Our proof resembles part of Helmers and van Zwet (1982), where an analogous result is obtained for the Student t ‐statistic. The present note extends this to Studentized U ‐statistics.