Exchangeable Sequences Driven by an Absolutely Continuous Random Measure

Patrizia Berti, Luca Pratelli and Pietro Rigo
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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

No 142, Quaderni di Dipartimento from University of Pavia, Department of Economics and Quantitative Methods

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].

Keywords: Conditional identity in distribution; Exchangeability; Predictive measure; Random probability measure. (search for similar items in EconPapers)
Pages: 11 pages
Date: 2011-03
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