An invariance principle for processes indexed by two parameters and some statistical applications

Manfred Heinz Denker, Madan L. Puri

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Let D((0 l] 2 ) denote the space of all functions on (0,l] 2 with no discontinuities of the second kind. We prove weak invariance principles in the space D((0,l] 2 ) for processes of the form ∫h(H n+m (t))dF n (t), 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 = (n+m+I) -1 (nF n + mG m ), and where h belongs to a certain class of functions on the open unit interval. The appropriate topology in D(((0,l] 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.

Original languageEnglish (US)
Title of host publicationProbability Theory and Extreme Value Theory
PublisherDe Gruyter Mouton
Pages310-361
Number of pages52
Volume2
ISBN (Electronic)9783110917826
ISBN (Print)9789067643856
StatePublished - Jul 11 2011

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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