Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/95338
Authors: 
Berti, Patrizia
Crimaldi, Irene
Pratelli, Luca
Rigo, Pietro
Year of Publication: 
2009
Series/Report no.: 
Quaderni di Dipartimento 091
Abstract: 
his paper deals with empirical processes of the type Cn(B) = n 1/2) {µn(B) - P(Xn+1 in BX1, . . . ,Xn)} , where (Xn) is a sequence of random variables and µn = (1/n)SUM(i=1,..,n) d(Xi) the empirical measure. Conditions for supBn(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 supBn(B) ->0 or even that n 1/2) supBn(B)converges a.s.. Results of this type are useful in Bayesian statistics.
Subjects: 
Bayesian predictive inference
Central limit theorem
Conditional identity in distribution
Empirical distribution
Exchangeability
Predictive distribution
Stable convergence
Document Type: 
Working Paper

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