relation: http://eprints.imtlucca.it/980/
title: Rate of convergence of predictive distributions for dependent data
creator: Berti, Patrizia
creator: Crimaldi, Irene
creator: Pratelli, Luca
creator: Rigo, Pietro
subject: HA Statistics
subject: QA Mathematics
description: This paper deals with empirical processes of the type    [C_{n}(B)=\sqrt{n}\{\mu_{n}(B)-P(X_{n+1}\in B\mid X_{1},\ldots,X_{n})\},\]    where (Xn) is a sequence of random variables and μn=(1/n)∑i=1nδXi 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 Berti et al. [Ann. Probab. 32 (2004) 2029–2052]). By such conditions, in some relevant situations, one obtains that $\sup_{B}|C_{n}(B)|\stackrel{P}{\rightarrow}0$ or even that $\sqrt{n}\sup_{B}|C_{n}(B)|$ converges a.s. Results of this type are useful in Bayesian statistics.  
publisher: Bernoulli Society for Mathematical Statistics and Probability
date: 2009
type: Article
type: PeerReviewed
identifier:   Berti, Patrizia and Crimaldi, Irene and Pratelli, Luca and Rigo, Pietro  Rate of convergence of predictive distributions for dependent data.  Bernoulli, 15 (4).  pp. 1351-1367.  ISSN 1350-7265      (2009)  
relation: http://projecteuclid.org/euclid.bj/1262962239
relation: 10.3150/09-BEJ191