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 language | English (US) |
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Pages (from-to) | 300-330 |
Number of pages | 31 |
Journal | Journal of Multivariate Analysis |
Volume | 43 |
Issue number | 2 |
DOIs | |
State | Published - Nov 1992 |
Externally published | Yes |
Keywords
- Poisson random field
- U-statistics
- interpoint distance
- k-clusters
- martingales
ASJC Scopus subject areas
- Statistics and Probability
- Numerical Analysis
- Statistics, Probability and Uncertainty