Product disintegrations: A law of large numbers via conditional independence

Luísa Borsato, Eduardo Horta and Rafael Rigão Souza

Statistics & Probability Letters, 2024, vol. 208, issue C

Abstract: 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.

Keywords: Law of large numbers; Random measure; Disintegration; Conditional independence (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110056

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