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Berti, Patrizia
Crimaldi, Irene
Pratelli, Luca
Rigo, Pietro
Year of Publication: 
Series/Report no.: 
Quaderni di Dipartimento 112
et (Xn) be a sequence of integrable real random variables, adapted to a filtration (Gn). Define: Cn = n 1/2) {1/n SUM(k=1:n) Xk - E(Xn+1 n) } and Dn = n 1/2){ E(Xn+1Gn)-Z } where Z is the a.s. limit of E(Xn+1 n) (assumed to exist). Conditions for (Cn,Dn) --> N(0,U) × N(0,V) stably are given, where U, V are certain random variables. In particular, under such conditions, one obtains n 1/2) { 1/n SUM(k=1:n) Xk - Z } = Cn + Dn --> N(0,U+V) stably. This CLT has natural applications to Bayesian statistics and urn problems. The latter are investigated, by paying special attention to multicolor randomly reinforced generalized Polya urns.
Bayesian statistics – Central limit theorem – Empirical distribution – Poisson-Dirichlet process – Predictive distribution – Random probability measure – Stable convergence – Urn model
Document Type: 
Working Paper

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