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

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Invariance Principle
Two Parameters
Weak Invariance Principle
Linear Rank Statistics
Nonparametric Statistics
Rank Statistics
Empirical Distribution Function
D-space
Uniform convergence
Signed
Compact Set
Identically distributed
Discontinuity
Random variable
Denote
Topology
Interval
Unit
Class
Form

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Denker, M. H., & Puri, M. L. (2011). An invariance principle for processes indexed by two parameters and some statistical applications. In Probability Theory and Extreme Value Theory (Vol. 2, pp. 310-361). De Gruyter Mouton.
Denker, Manfred Heinz ; Puri, Madan L. / An invariance principle for processes indexed by two parameters and some statistical applications. Probability Theory and Extreme Value Theory. Vol. 2 De Gruyter Mouton, 2011. pp. 310-361
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Denker, MH & Puri, ML 2011, An invariance principle for processes indexed by two parameters and some statistical applications. in Probability Theory and Extreme Value Theory. vol. 2, De Gruyter Mouton, pp. 310-361.

An invariance principle for processes indexed by two parameters and some statistical applications. / Denker, Manfred Heinz; Puri, Madan L.

Probability Theory and Extreme Value Theory. Vol. 2 De Gruyter Mouton, 2011. p. 310-361.

Research output: Chapter in Book/Report/Conference proceedingChapter

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Denker MH, Puri ML. An invariance principle for processes indexed by two parameters and some statistical applications. In Probability Theory and Extreme Value Theory. Vol. 2. De Gruyter Mouton. 2011. p. 310-361