On the order of magnitude of cumulants of von Mises functionals and related statistics

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

It is shown that under appropriate conditions the sth cumulant of a von Mises statistic or a U (or V) statistic is O(n -s+1 ), s ≥ 2, as the sample size n goes to infinity. A possible route toward the derivation of an asymptotic expansion of the characteristic function is indicated.

Original languageEnglish (US)
Title of host publicationProbability Theory and Extreme Value Theory
PublisherDe Gruyter Mouton
Pages54-62
Number of pages9
Volume2
ISBN (Electronic)9783110917826
ISBN (Print)9789067643856
StatePublished - Jul 11 2011
Externally publishedYes

Keywords

  • Edgeworth expansion
  • U-statistics
  • V-Statistics

ASJC Scopus subject areas

  • Mathematics(all)

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  • Cite this

    Bhattacharya, R. N., & Puri, M. L. (2011). On the order of magnitude of cumulants of von Mises functionals and related statistics. In Probability Theory and Extreme Value Theory (Vol. 2, pp. 54-62). De Gruyter Mouton.