Rate of convergence of predictive distributions for dependent data
| Autor: | Irene Crimaldi, Pietro Rigo, Patrizia Berti, Luca Pratelli |
|---|---|
| Přispěvatelé: | P. Berti, I. Crimaldi, L. Pratelli, P. Rigo |
| Rok vydání: | 2010 |
| Předmět: |
Statistics and Probability
convergence in distribution CENTRAL LIMIT THEOREM Conditional identity in distribution Central limit theorem Mathematics - Statistics Theory Statistics Theory (math.ST) Type (model theory) Empirical distribution Combinatorics ddc:330 FOS: Mathematics CONDITIONAL IDENTITY IN DISTRIBUTION Stable convergence Mathematics Bayesian predictive inference central limit theorem conditional identity in distribution empirical distribution exchangeability predictive distribution stable convergence Empirical distribution function EMPIRICAL DISTRIBUTION STABLE CONVERGENCE Distribution (mathematics) Rate of convergence Convergence of random variables MAT/06 Probabilità e statistica matematica Predictive distribution BAYESIAN PREDICTIVE INFERENCE Exchangeability Bayesian predictive inference Central limit theorem Conditional identity in distribution Empirical distribution Exchangeability Predictive distribution Stable convergence Random variable |
| Zdroj: | Berti, Patrizia ; Crimaldi, Irene ; Pratelli, Luca ; Rigo, Pietro (2008) Rate of convergence of predictive distributions for dependent data. [Preprint] Bernoulli 15, no. 4 (2009), 1351-1367 |
| DOI: | 10.48550/arxiv.1001.2152 |
| Popis: | This paper deals with empirical processes of the type \[C_n(B)=\sqrt{n}\{\mu_n(B)-P(X_{n+1}\in B\mid X_1,...,X_n)\},\] where $(X_n)$ is a sequence of random variables and $\mu_n=(1/n)\sum_{i=1}^n\delta_{X_i}$ the empirical measure. Conditions for $\sup_B|C_n(B)|$ to converge stably (in particular, in distribution) are given, where $B$ ranges over a suitable class of measurable sets. These conditions apply when $(X_n)$ 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 $\sup_B|C_n(B)|\stackrel{P}{\to}0$ or even that $\sqrt{n}\sup_B|C_n(B)|$ converges a.s. Results of this type are useful in Bayesian statistics. Comment: Published in at http://dx.doi.org/10.3150/09-BEJ191 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm) |
| Databáze: | OpenAIRE |
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