LIMIT LAWS FOR LARGE KTH-NEAREST NEIGHBOR BALLS

被引：5

作者：

Chenavier, Nicolas ^{[1
,4
]}

Henze, Norbert ^{[2
,5
]}

Otto, Moritz ^{[3
,6
]}

机构：

[1] Univ Littoral Cote dOpale, Dunkerque, France

[2] Karlsruhe Inst Technol KIT, Karlsruhe, Germany

[3] Otto von Guericke Univ, Magdeburg, Germany

[4] 50 Rue Ferdinand Buisson, F-62228 Calais, France

[5] Englerstr 2, D-76133 Karlsruhe, Germany

[6] Aarhus Univ, Ny Munkegade 118, DK-8000 Aarhus C, Denmark

来源：

JOURNAL OF APPLIED PROBABILITY | 2022年 / 59卷 / 03期

关键词：

Binomial point process; large kth nearest neighbor balls; Chen-Stein method; Poisson convergence; Gumbel distribution; DISTRIBUTIONS;

D O I：

10.1017/jpr.2021.92

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：

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 oo, 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.

引用

页码：880 / 894

页数：15

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