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Product disintegrations: A law of large numbers via conditional independence

Author

Listed:
  • Borsato, Luísa
  • Horta, Eduardo
  • Souza, Rafael Rigão

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.

Suggested Citation

  • Borsato, Luísa & Horta, Eduardo & Souza, Rafael Rigão, 2024. "Product disintegrations: A law of large numbers via conditional independence," Statistics & Probability Letters, Elsevier, vol. 208(C).
    • Handle: RePEc:eee:stapro:v:208:y:2024:i:c:s0167715224000257
    DOI: 10.1016/j.spl.2024.110056
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