Asymptotic distribution of the maximum interpoint distance for high-dimensional data

被引：2

作者：

Tang, Ping ^{[1
]}

Lu, Rongrong ^{[1
]}

Xie, Junshan ^{[1
]}

机构：

[1] Henan Univ, Sch Math & Stat, Kaifeng 475000, Peoples R China

来源：

STATISTICS & PROBABILITY LETTERS | 2022年 / 190卷

基金：

中国国家自然科学基金;

关键词：

Interpoint distance; Gumbel distribution; Stein-Chen Poisson approximation; Moderate deviation; LIKELIHOOD RATIO TESTS; LARGEST ENTRIES; LIMIT DISTRIBUTION; SAMPLE; LAWS; DIAMETER; THEOREMS; MATRICES;

D O I：

10.1016/j.spl.2022.109567

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 random sample coming from a p-dimensional population with independent sub-exponential components. Denote the maximum interpoint Euclidean distance by M-n = max(1 <= i <= jn) ?Xi-Xj?. When the dimension p=p(n)-> infinity with the sample size n -> infinity, it proves that M-n(2) under a suitable normalization asymptotically obeys a Gumbel type distribution. The proofs mainly depend on the Stein-Chen Poisson approximation method and the moderate deviation of the sum of independent random variables. (C) 2022 Published by Elsevier B.V.

引用

页数：7

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