Product disintegrations: A law of large numbers via conditional independence

被引：0

作者：

Borsato, Luisa ^{[1
]}

Horta, Eduardo ^{[2
]}

Souza, Rafael Rigao ^{[2
]}

机构：

[1] Univ Sao Paulo, Inst Math & Stat, 1010 Rua Matao, BR-05508090 Sao Paulo, SP, Brazil

[2] Univ Fed Rio Grande do Sul, Inst Math & Stat, 9500 Bento Goncalves Ave,43-111, BR-91509900 Porto Alegre, RS, Brazil

来源：

STATISTICS & PROBABILITY LETTERS | 2024年 / 208卷

基金：

巴西圣保罗研究基金会;

关键词：

Law of large numbers; Random measure; Disintegration; Conditional independence;

D O I：

10.1016/j.spl.2024.110056

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 introduce the concept of a product disintegration, which generalizes exchangeability by allowing one to render conditional independence in terms of a suitable hidden sequence of random probabilities. We prove that, given a sequence of random elements in a compact metric space, a strong law of large numbers (SLLN) holds for observables of this process if and only if the process admits a product disintegration that itself satisfies a type of SLLN. As an application, we provide a characterization of the SLLN for identically distributed (not necessarily independent) Bernoulli sequences.

引用

页数：4

共 9 条

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