Necessary and sufficient conditions for the strong law of large numbers for U-statistics

Authors
Latala, R Zinn, J
Citation
R. Latala et J. Zinn, Necessary and sufficient conditions for the strong law of large numbers for U-statistics, ANN PROBAB, 28(4), 2000, pp. 1908-1924
Citations number
13
Categorie Soggetti
Mathematics
Journal title
ANNALS OF PROBABILITY
ISSN journal
00911798 → ACNP
Volume
28
Issue
4
Year of publication
2000
Pages
1908 - 1924
Database
ISI
SICI code
0091-1798(200010)28:4<1908:NASCFT>2.0.ZU;2-R
Abstract
Under some mild regularity on the normalizing sequence, we obtain necessary and sufficient conditions for the strong law of large numbers for (symmetr ized) U-statistics. We also obtain necessary and sufficient conditions for the a.s. convergence of series of an analogous form.