Invariance principles for von Mises and U-statistics

Herold Dehling; Manfred Denker; Walter Philipp

doi:10.1007/BF00535265

Invariance principles for von Mises and U-statistics

Herold Dehling
, Manfred Denker
, Walter Philipp

Mathematics

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

The almost sure approximation of von Mises-statistics and U-statistics by appropriate stochastic integrals with respect to Kiefer processes is obtained. In general these integrals are non-Gaussian processes. As applications we get almost sure versions for the estimator of the variance and for the χ²-test of goodness of fit.

Original language	English (US)
Pages (from-to)	139-167
Number of pages	29
Journal	Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Volume	67
Issue number	2
DOIs	https://doi.org/10.1007/BF00535265
State	Published - Jun 1984

All Science Journal Classification (ASJC) codes

Analysis
Statistics and Probability
General Mathematics

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title = "Invariance principles for von Mises and U-statistics",

abstract = "The almost sure approximation of von Mises-statistics and U-statistics by appropriate stochastic integrals with respect to Kiefer processes is obtained. In general these integrals are non-Gaussian processes. As applications we get almost sure versions for the estimator of the variance and for the χ2-test of goodness of fit.",

author = "Herold Dehling and Manfred Denker and Walter Philipp",

year = "1984",

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T1 - Invariance principles for von Mises and U-statistics

AU - Dehling, Herold

AU - Denker, Manfred

AU - Philipp, Walter

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AB - The almost sure approximation of von Mises-statistics and U-statistics by appropriate stochastic integrals with respect to Kiefer processes is obtained. In general these integrals are non-Gaussian processes. As applications we get almost sure versions for the estimator of the variance and for the χ2-test of goodness of fit.

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SN - 0044-3719

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IS - 2

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Invariance principles for von Mises and U-statistics

Abstract

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