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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 9, Fasc. 1,
pages 25 - 76
 

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

Manfred Denker
Madan L. Puri

Abstract: Let D((0,1]2) denote the space of all functions on (0,1]2 with no discontinuities of the second kind. We prove weak invariance principles in the space D((0,1]2) for processes of the form integral h(H (t))dF (t), n+m n m, n > 1, where F n and G m are two independent empirical distribution functions of independent, identically distributed sequences of random variables,

H = (n +m +1)-1(nF + mG ), n+m n m
and where h belongs to a certain class of functions on the open unit interval. The appropriate topology in D((0,1]2) 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: -

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