Invariance principles for von Mises and U-statistics

Herold Dehling, Manfred Heinz Denker, Walter Philipp

Research output: Contribution to journalArticle

21 Citations (Scopus)

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

Fingerprint

Kiefer Process
U-statistics
Invariance Principle
Stochastic Integral
Goodness of fit
Statistics
Estimator
Approximation
Integral
Invariance

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Mathematics(all)

Cite this

Dehling, Herold ; Denker, Manfred Heinz ; Philipp, Walter. / Invariance principles for von Mises and U-statistics. In: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete. 1984 ; Vol. 67, No. 2. pp. 139-167.
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Invariance principles for von Mises and U-statistics. / Dehling, Herold; Denker, Manfred Heinz; Philipp, Walter.

In: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 67, No. 2, 01.06.1984, p. 139-167.

Research output: Contribution to journalArticle

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