Invariance principles for von Mises and U-statistics

Herold Dehling, Manfred Heinz Denker, Walter Philipp

Research output: Contribution to journalArticle

21 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 χ 2 -test of goodness of fit.

Original languageEnglish (US)
Pages (from-to)139-167
Number of pages29
JournalZeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Volume67
Issue number2
DOIs
StatePublished - Jun 1 1984

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Mathematics(all)

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