Exchangeable sequences driven by an absolutely continuous random measure

• Patrizia Berti ^[1] ; Luca Pratelli ^[2] ; Pietro Rigo ^[3]
  1. [1] Universita' di Modena e Reggio-Emilia
  2. [2] Accademia Navale di Livorno
  3. [3] Universita' di Pavia

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• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 3, 2, 2013, págs. 2090-2102
• Idioma: inglés
• DOI: 10.1214/12-AOP786
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let S be a Polish space and (Xn:n≥1) an exchangeable sequence of S-valued random variables. Let αn(⋅)=P(Xn+1∈⋅∣X1,…,Xn) be the predictive measure and α a random probability measure on S such that αn⟶weakα a.s. Two (related) problems are addressed. One is to give conditions for α≪λ a.s., where λ is a (nonrandom) σ-finite Borel measure on S. Such conditions should concern the finite dimensional distributions L(X1,…,Xn), n≥1, only. The other problem is to investigate whether ∥αn−α∥⟶a.s.0, where ∥⋅∥ is total variation norm. Various results are obtained. Some of them do not require exchangeability, but hold under the weaker assumption that (Xn) is conditionally identically distributed, in the sense of [Ann. Probab. 32 (2004) 2029–2052].