AN INVARIANCE PRINCIPLE FOR PROCESSES INDEXED BY TWO
PARAMETERS AND SOME STATISTICAL APPLICATIONS

Manfred Denker

Madan L. Puri

Abstract: Let denote the space of all functions on with no discontinuities
of the second kind. We prove weak invariance principles in the space for
processes of the form where and are two
independent empirical distribution functions of independent, identically distributed sequences
of random variables,

and
where

belongs to a certain class of functions on the open unit interval. The appropriate
topology in

is given by uniform convergence on compact sets. This type of
processes is central in nonparametric statistics having applications to two-sample linear rank
statistics and signed rank statistics.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -