TY  - JOUR
EP  - 546
ID  - eprints975
UR  - http://projecteuclid.org/euclid.jap/1308662642
KW  - Bayesian statistics; central limit theorem; empirical distribution; Poisson-Dirichlet process; predictive distribution; random probability measure; stable convergence; urn model
TI  - A central limit theorem and its applications to multicolor randomly reinforced urns
AV  - none
N2  - Let Xn be a sequence of integrable real random variables, adapted to a filtration (Gn). Define Cn = ?{(1 / n)?k=1nXk - E(Xn+1 | Gn)} and Dn = ?n{E(Xn+1 | Gn) - Z}, where Z is the almost-sure limit of E(Xn+1 | Gn) (assumed to exist). Conditions for (Cn, Dn) ? N(0, U) x N(0, V) stably are given, where U and V are certain random variables. In particular, under such conditions, we obtain ?n{(1 / n)?k=1nX_k - Z} = Cn + Dn ? N(0, U + V) stably. This central limit theorem has natural applications to Bayesian statistics and urn problems. The latter are investigated, by paying special attention to multicolor randomly reinforced urns. 
SN  - 0021-9002
VL  - 48
JF  - Journal of applied probability 
IS  - 2
Y1  - 2011///
SP  - 527
PB  - Applied Probability Trust
A1  - Berti, Patrizia
A1  - Crimaldi, Irene
A1  - Pratelli, Luca
A1  - Rigo, Pietro
ER  -