Rate of Convergence of Predictive Distributions for Dependent Data

Patrizia Berti, Irene Crimaldi, Luca Pratelli and Pietro Rigo
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Patrizia Berti: Department of Mathematics, University of Modena and Reggio Emilia
Irene Crimaldi: Department of Mathematics, University of Bologna
Luca Pratelli: Accademia Navale di Livorno
Pietro Rigo: Department of Economics and Quantitative Methods, University of Pavia

No 91, Quaderni di Dipartimento from University of Pavia, Department of Economics and Quantitative Methods

Abstract: This paper deals with empirical processes of the type Cn(B) = n^(1/2) {µn(B) - P(Xn+1 in B | X1, . . . ,Xn)} , where (Xn) is a sequence of random variables and µn = (1/n)SUM(i=1,..,n) d(Xi) the empirical measure. Conditions for supB|Cn(B)| to converge stably (in particular, in distribution) are given, where B ranges over a suitable class of measurable sets. These conditions apply when (Xn) is exchangeable, or, more generally, conditionally identically distributed (in the sense of [6]). By such conditions, in some relevant situations, one obtains that supB|Cn(B)|-P->0 or even that n^(1/2) supB|Cn(B)| converges a.s.. Results of this type are useful in Bayesian statistics.

Keywords: Bayesian predictive inference; Central limit theorem; Conditional identity in distribution; Empirical distribution; Exchangeability; Predictive distribution; Stable convergence. (search for similar items in EconPapers)
Pages: 15 pages
Date: 2009-01
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Citations: View citations in EconPapers (3)

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