Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series A, Pt. 2 , pp. 179--194

UNIFORM STRONG CONSISTENCY RATES FOR CONDITIONAL *U*-STATISTICS

By

ARUSHARKA SEN, *Indian Statistical Institute*

SUMMARY. Let (X_{i}, Y_{i})^{n}_{i=1} be a random sample from a bivariate distribution. We want to estimate m(** t**): E(h(Y

*AMS (1990) subject classification.* Primary 62G07; secondary 62G20, 60F15.

*Key words and phrases.* Conditional $U$-statistics, uniform strong consistency, empirical processes of $U$-statistic structure, Vapnik-Cervonenkis theory, $V-C$ graph class, deviation measurability.