Moderate deviations for Ewens-Pitman exchangeable random partitions

Stefano Favaro; Shui Feng; Fuqing Gao

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arXiv · 1610.03328

Moderate deviations for Ewens-Pitman exchangeable random partitions

Stefano Favaro·Shui Feng·Fuqing Gao

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Abstract

Consider a population of individuals belonging to an infinity number of types, and assume that type proportions follow the two-parameter Poisson-Dirichlet distribution. A sample of size n is selected from the population. The total number of different types and the number of types appearing in the sample with a fixed frequency are important statistics. In this paper we establish the moderate deviation principles for these quantities. The corresponding rate functions are explicitly identified, which help revealing a critical scale and understanding the exact role of the parameters. Conditional, or posterior, counterparts of moderate deviation principles are also established.

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Stefano Favaro, Shui Feng, Fuqing Gao. 2016-10-11. Moderate deviations for Ewens-Pitman exchangeable random partitions. https://arxiv.org/abs/1610.03328

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