Central Limit Theorems For Multicolor Urns With Dominated Colors

Patrizia Berti, Irene Crimaldi, Luca Pratelli and Pietro Rigo
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Patrizia Berti: Università di Modena e 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 106, Quaderni di Dipartimento from University of Pavia, Department of Economics and Quantitative Methods

Abstract: 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 An =diag (An,1, . . . ,An,d) be the n-th reinforce matrix. Assuming EAn,j = EAn,1 for all n and j, a few CLT’s are available for such urns. In real problems, however, it is more reasonable to assume EAn,j = EAn,1 whenever n >= 1 and 1 limsup EAn,j whenever j > d0, for some integer 1 = 1) is independent but need not be identically distributed. Some statistical applications are given as well.

Keywords: Central limit theorem; Clinical trials; Random probability measure; Stable convergence; Urn model. (search for similar items in EconPapers)
Pages: 18 pages
Date: 2009-12
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