LIMIT LAWS FOR LARGE kTH-NEAREST NEIGHBOR BALLS
Résumé
Let X 1 , X 2 ,. .. , X n be a sequence of independent random points in R d with common Lebesgue density f. Under some conditions on f , we obtain a Poisson limit theorem, as n → ∞, for the number of large probability kth-nearest neighbor balls of X 1 ,. .. , X n. Our result generalizes Theorem 2.2 of [11], which refers to the special case k = 1. Our proof is completely different since it employs the Chen-Stein method instead of the method of moments. Moreover, we obtain a rate of convergence for the Poisson approximation.
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