Bhattacharya, Rabi N. ; Ghosh, Jayanta K. (1992) A class of U-statistics and asymptotic normality of the number of k-clusters Journal of Multivariate Analysis, 43 (2). pp. 300-330. ISSN 0047-259X
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Official URL: http://linkinghub.elsevier.com/retrieve/pii/004725...
Related URL: http://dx.doi.org/10.1016/0047-259X(92)90038-H
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.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier Science. |
| Keywords: | U-statistics; Martingales; Interpoint Distance; Poisson Random Field; k-clusters |
| ID Code: | 22540 |
| Deposited On: | 24 Nov 2010 08:22 |
| Last Modified: | 02 Jun 2011 07:12 |
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