A Central Limit Theorem and Its Applications to Multicolor Randomly Reinforced Urns

Patrizia Berti, Irene Crimaldi, Luca Pratelli and Pietro Rigo
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Patrizia Berti: Department of Mathematics, University of Modena and Reggio Emilia
Irene Crimaldi: Università di Bologna
Luca Pratelli: Accademia Navale di Livorno
Pietro Rigo: Department of Economics and Quantitative Methods, University of Pavia

No 112, Quaderni di Dipartimento from University of Pavia, Department of Economics and Quantitative Methods

Abstract: Let (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 | Gn) } and Dn = n^(1/2){ E(Xn+1 | Gn)-Z } where Z is the a.s. limit of E(Xn+1 | Gn) (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.

Keywords: Bayesian; statistics; –; Central; limit; theorem; –; Empirical; distribution; –; Poisson-Dirichlet; process; –; Predictive; distribution; –; Random; probability; measure; –; Stable; convergence; –; Urn; model. (search for similar items in EconPapers)
Pages: 19 pages
Date: 2010-11
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Citations: View citations in EconPapers (2)

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