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)

## Abstract

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.

Item Type: | Article |
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Identification Number: | 10.3150/09-BEJ191 |

Uncontrolled Keywords: | Bayesian predictive inference; central limit theorem; conditional identity in distribution; empirical distribution; exchangeability; predictive distribution; stable convergence |

Subjects: | H Social Sciences > HA Statistics Q Science > QA Mathematics |

Research Area: | Economics and Institutional Change |

Depositing User: | Irene Crimaldi |

Date Deposited: | 31 Oct 2011 13:28 |

Last Modified: | 03 Nov 2011 13:19 |

URI: | http://eprints.imtlucca.it/id/eprint/980 |

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