Weak convergence of row and column exchangeable arrays

Abstract

Sufficient conditions are given to ensure the partial sum process of a sequence of row and column exchangeable arrays converges to a Brownian motion on [0,l]². The results are then applied to obtain limit results for generalized U-statistics based on samples from finite populations

Keywords:

• Row and column exchangeable arrays
• two dimensional Brownian motion martingale
• generalized U-statistics

^*Research supported by a grant from the Natural Sciences and Engineering Research Council of Canada.

^*Research supported by a grant from the Natural Sciences and Engineering Research Council of Canada.

Notes

^*Research supported by a grant from the Natural Sciences and Engineering Research Council of Canada.