A class of \(U\)-statistics and asymptotic normality of the number of \(k\)- clusters
type: Item
instance of: scholarly article
title: A class of \(U\)-statistics and asymptotic normality of the number of \(k\)- clusters
zbMATH Open document ID: 0764.60025
DOI: 10.1016/0047-259X(92)90038-H
author: Rabi Bhattacharya
author: Jayanta K. Ghosh
published in: Journal of Multivariate Analysis
publication date: 1993-04-01T00:00:00Z
review text: The authors prove a central limit theorem for a class of \(U\)-statistics whose kernel depends on the sample size and for which the projection method may fail. As an application they derive the asymptotic normality of the number of Poisson \(K\)-clusters in a cube of increasing size in \(R^ d\). In this process they also extend earlier results of \textit{S. R. Jammalamadaka} and \textit{S. Janson} [Ann. Probab. 14, 1347-1358 (1986; Zbl 0604.60023)] to general kernels and to general orders \(K>2\) of the kernel.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 148933
zbMATH Keywords: central limit theorem
zbMATH Keywords: \(U\)-statistics
zbMATH Keywords: asymptotic normality
reviewed by: Adhir K. Basu
MaRDI profile type: Publication
cites work: Q3998410
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full work available at URL: 0047-259x(92)90038-h
OpenAlex ID: W1976237433
description: scientific article; zbMATH DE number 148933