TY  - JOUR
UR  - http://www.sciencedirect.com/science/article/pii/S0304414910001109
KW  - Central limit theorem; Clinical trials; Random probability measure; Stable convergence; Urn model
TI  - Central limit theorems for multicolor urns with dominated colors
AV  - public
N2  - An urn contains balls of d?2 colors. At each time n?1, a ball is drawn and then replaced together with a random number of balls of the same color. Let A n = diag (An,1,?,An,d) be the n-th reinforce matrix. Assuming that EAn,j=EAn,1 for all n and j, a few central limit theorems (CLTs) are available for such urns. In real problems, however, it is more reasonable to assume that EA n,j = EA n,1 whenever  n ? 1  and  1 ? j ? d0 , liminfn EAn,1 > limsupn EAn,j whenever  j > d0  for some integer 1?d0?d. Under this condition, the usual weak limit theorems may fail, but it is still possible to prove the CLTs for some slightly different random quantities. These random quantities are obtained by neglecting dominated colors, i.e., colors from d0+1 to d, and they allow the same inference on the urn structure. The sequence (An : n ? 1) is independent but need not be identically distributed. Some statistical applications are given as well.
SN  - 0304-4149
EP  - 1491
ID  - eprints978
JF  - Stochastic processes and their applications 
IS  - 8
Y1  - 2010/08//
SP  - 1473
PB  - Elsevier
A1  - Berti, Patrizia
A1  - Crimaldi, Irene
A1  - Pratelli, Luca
A1  - Rigo, Pietro
VL  - 120
ER  -