A class of U-statistics and asymptotic normality of the number of k-clusters

Rabindra N Bhattacharya, Jayanta K. Ghosh

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

A central limit theorem is proved for a class of U-statistics whose kernel depends on the sample size and for which the projection method may fail, since several terms in the Hoeffding decomposition contribute to the limiting variance. As an application we derive the asymptotic normality of the number of Poisson k-clusters in a cube of increasing size in Rd. We also extend earlier results of Jammalamadaka and Janson to general kernels and to general orders k > 2 of the kernel.

Original languageEnglish (US)
Pages (from-to)300-330
Number of pages31
JournalJournal of Multivariate Analysis
Volume43
Issue number2
DOIs
StatePublished - 1992
Externally publishedYes

Fingerprint

U-statistics
Asymptotic Normality
Statistics
kernel
Decomposition
Projection Method
Central limit theorem
Regular hexahedron
Siméon Denis Poisson
Sample Size
Limiting
Decompose
Term
Class
Kernel
Asymptotic normality

Keywords

  • interpoint distance
  • k-clusters
  • martingales
  • Poisson random field
  • U-statistics

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Numerical Analysis
  • Statistics and Probability

Cite this

A class of U-statistics and asymptotic normality of the number of k-clusters. / Bhattacharya, Rabindra N; Ghosh, Jayanta K.

In: Journal of Multivariate Analysis, Vol. 43, No. 2, 1992, p. 300-330.

Research output: Contribution to journalArticle

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