ON INTEGRABILITY IN THE LIL FOR DEGENERATE U-STATISTICS

Authors
GINE E ZHANG CH
Citation
E. Gine et Ch. Zhang, ON INTEGRABILITY IN THE LIL FOR DEGENERATE U-STATISTICS, Journal of theoretical probability, 9(2), 1996, pp. 385-412
Citations number
13
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Journal of theoretical probability → ACNP
ISSN journal
08949840
Volume
9
Issue
2
Year of publication
1996
Pages
385 - 412
Database
ISI
SICI code
0894-9840(1996)9:2<385:OIITLF>2.0.ZU;2-O
Abstract
It is shown by example that square integrability of the kennel h of a completely degenerate U-statistic is not a necessary condition for the law of the iterated logarithm to hold. Necessary integrability condit ions are given on ii which are in a sense the strongest possible. Suff icient conditions for a degenerate U-statistic of order 2 to satisfy t he LIL, weaker than square integrability of the kernel, are also given .