The probabilities of large deviations for a certain class of statistics associated with multinomial distribution

Mirakhmedov, Sherzod M.

ESAIM: Probability and Statistics, Tome 24 (2020), pp. 581-606.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

Let η = (η₁, …, η$$) be a multinomial random vector with parameters n = η₁ + ⋯ + η$$ and p$$ > 0, m = 1, …, N, p₁ + ⋯ + p$$ = 1. We assume that N →∞ and maxp$$ → 0 as n →∞. The probabilities of large deviations for statistics of the form h₁(η₁) + ⋯ + h$$(η$$) are studied, where h$$(x) is a real-valued function of a non-negative integer-valued argument. The new large deviation results for the power-divergence statistics and its most popular special variants, as well as for several count statistics are derived as consequences of the general theorems.

Classification : 60F10, 62E20, 62G20
Mots-clés : Chi-square statistic, count statistics, log-likelihood ration statistic, large deviations, multinomial distribution, Poisson distribution, power divergence statistics

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