Bounds for the concentration of asymptotically normal statistics

Authors
Alberink, IB Bentkus, V
Citation
Ib. Alberink et V. Bentkus, Bounds for the concentration of asymptotically normal statistics, ACT APPL MA, 58(1-3), 1999, pp. 11-59
Citations number
32
Categorie Soggetti
Mathematics
Journal title
ACTA APPLICANDAE MATHEMATICAE
ISSN journal
01678019 → ACNP
Volume
58
Issue
1-3
Year of publication
1999
Pages
11 - 59
Database
ISI
SICI code
0167-8019(199909)58:1-3<11:BFTCOA>2.0.ZU;2-L
Abstract
Let X-1, ..., X-n be independent, not necessarily identically distributed r andom variables. An optimal bound is derived for the concentration function of an arbitrary real-valued statistic T = T (X-1,..., X-n) for which ET2 < infinity. Applications are given for Wilcoxon's rank-sum statistic, U-stat istics, Student's statistic, the two-sample Student statistic and linear re gression.