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Exchangeable Sequences Driven by an Absolutely Continuous Random Measure

Author

Listed:
  • Patrizia Berti

    (Department of Mathematics, University of Modena and Reggio Emilia)

  • Luca Pratelli

    (Accademia Navale di Livorno)

  • Pietro Rigo

    (Department of Economics and Quantitative Methods, University of Pavia)

Abstract

Let S be a Polish space and (Xn : n = 1) an exchangeable sequence of S-valued random variables. Let an(·) = P( Xn+1 in · | X1, . . . ,Xn) be the predictive measure and a a random probability measure on S such that an (weak) --> a a.s.. Two (related) problems are addressed. One is to give conditions for a 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 [2].

Suggested Citation

  • Patrizia Berti & Luca Pratelli & Pietro Rigo, 2011. "Exchangeable Sequences Driven by an Absolutely Continuous Random Measure," Quaderni di Dipartimento 142, University of Pavia, Department of Economics and Quantitative Methods.
    • Handle: RePEc:pav:wpaper:142
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