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Prediction rules for exchangeable sequences related to species sampling

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  • Hansen, Ben
  • Pitman, Jim

Abstract

Suppose an exchangable sequence with values in a nice measurable space S admits a prediction rule of the following form: given the first n terms of the sequence, the next term equals the jth distinct value observed so far with probability pj,n, for j=1,2,... , and otherwise is a new value with distribution [nu] for some probability measure [nu] on S with no atoms. Then the pj,n depend only on the partitition of the first n integers induced by the first n values of the sequence. All possible distributions for such an exchangeable sequence are characterized in terms of constraints on the pj,n and in terms of their de Finetti representations.

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Bibliographic Info

Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 46 (2000)
Issue (Month): 3 (February)
Pages: 251-256

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Handle: RePEc:eee:stapro:v:46:y:2000:i:3:p:251-256

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Keywords: Exchangeable sequence Prediction rule Species sampling;

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Cited by:
  1. Masanao Aoki & Hiroshi Yoshikawa, 2012. "Non-self-averaging in macroeconomic models: a criticism of modern micro-founded macroeconomics," Journal of Economic Interaction and Coordination, Springer, vol. 7(1), pages 1-22, May.
  2. U. Garibaldi & D. Costantini & P. Viarengo, 2007. "The two-parameter Ewens distribution: a finitary approach," Journal of Economic Interaction and Coordination, Springer, vol. 2(2), pages 147-161, December.
  3. Andrea Collevecchio & Codina Cotar & Marco LiCalzi, 2011. "On a preferential attachment and generalized Pólya's urn model," Working Papers 8, Department of Management, Università Ca' Foscari Venezia, revised Oct 2012.
  4. Cerquetti, Annalisa, 2007. "A note on Bayesian nonparametric priors derived from exponentially tilted Poisson-Kingman models," Statistics & Probability Letters, Elsevier, vol. 77(18), pages 1705-1711, December.
  5. Bissiri, Pier Giovanni, 2010. "Characterization of the law of a finite exchangeable sequence through the finite-dimensional distributions of the empirical measure," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1306-1312, September.

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