A functional central limit theorem for the empirical Ripley's K-function

被引：3
|
作者：
Biscio, Christophe A. N. [1 ]
Svane, Anne Marie [1 ]
机构：
[1] Aalborg Univ, Dept Math Sci, Skjernvej 4A, DK-9220 Aalborg, Denmark
来源：
ELECTRONIC JOURNAL OF STATISTICS | 2022年 / 16卷 / 01期
关键词：
Point processes; Gibbs point processes; Ripley's K function; functional central limit theorem; goodness-of-fit test; PERFECT SIMULATION; TESTS;
D O I：
10.1214/22-EJS2017
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：
We establish a functional central limit theorem for the empirical Ripley's K-function of Gibbs point processes and point processes with fast decay of correlations. Our theorem greatly extend past results that were restricted to the Poisson case and allow to determine the asymptotic behaviour of statistics based on the K-function which may be used, for example, to develop goodness-of-fit tests. We illustrate this in a simulation study.
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页码：3060 / 3098
页数：39
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