Moderate Deviations for Ewens-Pitman Sampling Models

Autor:	Shui Feng, Stefano Favaro, Fuqing Gao
Rok vydání:	2018
Předmět:	Statistics and Probability Combinatorics education.field_of_study Distribution (mathematics) Population Sampling (statistics) Sample (statistics) Scale (descriptive set theory) Moderate deviations Statistics Probability and Uncertainty Type (model theory) education Mathematics
Zdroj:	Sankhya A. 80:330-341
ISSN:	0976-8378 0976-836X
DOI:	10.1007/s13171-018-0124-z
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::a2350db8a05849203837d000040d606e https://doi.org/10.1007/s13171-018-0124-z Zobrazit plný text záznamu Full text from SpringerLink