Moderate Deviations for Ewens-Pitman Sampling Models

Stefano Favaro (), Shui Feng () and Fuqing Gao ()
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Stefano Favaro: University of Torino and Collegio Carlo Alberto
Shui Feng: McMaster University
Fuqing Gao: Wuhan University

Sankhya A: The Indian Journal of Statistics, 2018, vol. 80, issue 2, No 7, 330-341

Abstract: 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.

Keywords: α-diversity; Large and moderate deviations; Poisson-Dirichlet distribution; Random partition; Primary 60F05; Secondary 60G57 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s13171-018-0124-z

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