A REMARK ON CONVERGENCE IN DISTRIBUTION OF U-STATISTICS

Authors
GINE E ZINN J
Citation
E. Gine et J. Zinn, A REMARK ON CONVERGENCE IN DISTRIBUTION OF U-STATISTICS, Annals of probability, 22(1), 1994, pp. 117-125
Citations number
12
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Annals of probability → ACNP
ISSN journal
00911798
Volume
22
Issue
1
Year of publication
1994
Pages
117 - 125
Database
ISI
SICI code
0091-1798(1994)22:1<117:AROCID>2.0.ZU;2-R
Abstract
It is proved that, for h measurable and symmetric in its arguments and X(i) i.i.d., if the sequence (n(-m/2)SIGMA(i1,...,im less-than-or-equ al-to n, ij not-equal ik if j not-equal k) h(X(i1),...,X(im))}n=1infin ity is stochastically bounded, then Eh2 < infinity and Eh(X1,x2,...,x( m)) = 0 a.s..