A CLASS OF U-STATISTICS AND ASYMPTOTIC NORMALITY OF THE NUMBER OF K-CLUSTERS

被引：15

作者：

BHATTACHARYA, RN ^{[1
]}

GHOSH, JK ^{[1
]}

机构：

[1] PURDUE UNIV, W LAFAYETTE, IN 47907 USA

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 1992年 / 43卷 / 02期

关键词：

U-STATISTICS; MARTINGALES; INTERPOINT DISTANCE; POISSON RANDOM FIELD; K-CLUSTERS;

D O I：

10.1016/0047-259X(92)90038-H

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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. © 1992.

引用

页码：300 / 330

页数：31

共 10 条

[1]

Bhattacharya RN., 1990, STOCHASTIC PROCESSES

[2] A CENTRAL-LIMIT-THEOREM FOR GENERALIZED MULTILINEAR FORMS [J].