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

Let η = ( η 1 , …, η N ) be a multinomial random vector with parameters n = η 1 + ⋯ + η N and p m > 0, m = 1, …, N , p 1 + ⋯ + p N = 1. We assume that N → ∞ and max p m → 0 as n → ∞ . The probabilities of large deviations for statistics of the form h 1 ( η 1 ) + ⋯ + h N ( η N ) are studied, where h m ( 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.

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