A precise local limit theorem for the multinomial distribution

01/23/2020

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by   Frédéric Ouimet, et al.

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We develop a precise local limit theorem for the multinomial distribution where the error terms are explicit up to an order smaller than previous known results by a factor of N^1/2. We show how it can be used to approximate multinomial probabilities on most subsets of R^d and we also describe potential applications related to asymptotic properties of Bernstein estimators on the simplex, bounds for the deficiency distance with multivariate normal experiments and finely tuned continuity corrections.