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Moderate Deviations for Ewens-Pitman Sampling Models

Author

Listed:
  • Stefano Favaro

    (University of Torino and Collegio Carlo Alberto)

  • Shui Feng

    (McMaster University)

  • Fuqing Gao

    (Wuhan University)

Abstract

Consider a population of individuals belonging to an infinity number of types, and assume that type proportions follow the Poisson-Dirichlet distribution with parameter α ∈ [0,1) and 𝜃 > −α. Given a sample of size n from the population, two important statistics are the number Kn of different types in the sample, and the number Ml,n of different types with frequency l in the sample. We establish moderate deviation principles for (Kn)n≥ 1 and (Ml,n)n≥ 1. Corresponding rate functions are explicitly identified, which help in revealing a critical scale and in understanding the exact role of the parameters α and 𝜃.

Suggested Citation

  • Stefano Favaro & Shui Feng & Fuqing Gao, 2018. "Moderate Deviations for Ewens-Pitman Sampling Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 330-341, August.
    • Handle: RePEc:spr:sankha:v:80:y:2018:i:2:d:10.1007_s13171-018-0124-z
    DOI: 10.1007/s13171-018-0124-z
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    References listed on IDEAS

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    1. Stefano Favaro & Antonio Lijoi & Ramsés H. Mena & Igor Prünster, 2009. "Bayesian nonparametric inference for species variety with a two parameter Poisson-Dirichlet process prior," Carlo Alberto Notebooks 123, Collegio Carlo Alberto.
    2. Antonio Lijoi & Igor Pruenster & Stephen G. Walker, 2008. "Bayesian nonparametric estimators derived from conditional Gibbs structures," ICER Working Papers - Applied Mathematics Series 06-2008, ICER - International Centre for Economic Research.
    3. Stefano Favaro & Antonio Lijoi & Ramsés H. Mena & Igor Prünster, 2009. "Bayesian non‐parametric inference for species variety with a two‐parameter Poisson–Dirichlet process prior," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 993-1008, November.
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    Cited by:

    1. Alves, Caio & Ribeiro, Rodrigo & Valesin, Daniel, 2023. "Asymptotic results of a multiple-entry reinforcement process," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 451-489.

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