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Central Limit Theorems For Multicolor Urns With Dominated Colors

Author

Listed:
  • 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)

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.

Suggested Citation

  • Patrizia Berti & Irene Crimaldi & Luca Pratelli & Pietro Rigo, 2009. "Central Limit Theorems For Multicolor Urns With Dominated Colors," Quaderni di Dipartimento 106, University of Pavia, Department of Economics and Quantitative Methods.
    • Handle: RePEc:pav:wpaper:106
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    References listed on IDEAS

    as
    1. Janson, Svante, 2004. "Functional limit theorems for multitype branching processes and generalized Pólya urns," Stochastic Processes and their Applications, Elsevier, vol. 110(2), pages 177-245, April.
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