WEAK-CONVERGENCE FOR RECTANGLES-INDEXED WEIGHTED EMPIRICAL U-STATISTIC UNDER MIXING CONDITIONS

We have established in [3] the weak convergence of the weighted multivariate empirical U-statistic indexed by points under mixing conditions. In this paper we extend these results to the convergence of the weighted empirical U-statistic indexed by rectangles of [0, 1](p) with respect to the Skorohod topology in (D) over bar(p) space of functions indexed by rectangles introduced by Harel and Puri [2]. Applications to Cramer-Von Mises type and Anderson-Darling type statistics are given.