The class of tenable zero-balanced Pólya urns with an initially dominant subset of colors |
| |
Authors: | Sanaa Kholfi Hosam M Mahmoud |
| |
Institution: | Department of Statistics, The George Washington University, Washington, DC 20052, USA |
| |
Abstract: | In Kholfi and Mahmoud (2011) the class of tenable irreducible nondegenerate zero-balanced Pólya urn schemes is introduced and its asymptotic behavior in various phases is studied. In the absence of an initially dominant subset of colors, the counts of balls of all the colors satisfy multivariate central limit theorems. It is reported there that the case of an initially dominant subset of colors poses challenges requiring finer asymptotic analysis. In the present investigation we follow up on this. Indeed, we characterize noncritical cases with an initially dominant subset of colors in which not all ball counts satisfy one multivariate central limit theorem, but rather a subset of the ball counts satisfies a singular multivariate central limit theorem. The rest of the cases are critical, in which all the ball counts satisfy a multivariate central limit theorem, but under a different scaling. However, for these critical cases the Gaussian phases are delayed considerably. |
| |
Keywords: | 60C05 60F05 05A05 60G42 60G48 60E05 |
本文献已被 ScienceDirect 等数据库收录! |
|