Volume 24, 2020
|Page(s)||581 - 606|
|Published online||09 October 2020|
The probabilities of large deviations for a certain class of statistics associated with multinomial distribution
Institute of Mathematics, Academy of Sciences of Uzbekistan,
Mirzo Ulugbek str., 81,
* Corresponding author: firstname.lastname@example.org
Accepted: 3 August 2020
Let η = (η1, …, ηN) be a multinomial random vector with parameters n = η1 + ⋯ + ηN and pm > 0, m = 1, …, N, p1 + ⋯ + pN = 1. We assume that N →∞ and maxpm → 0 as n →∞. The probabilities of large deviations for statistics of the form h1(η1) + ⋯ + hN(ηN) are studied, where hm(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.
Mathematics Subject Classification: 60F10 / 62E20 / 62G20
Key words: Chi-square statistic / count statistics / log-likelihood ration statistic / large deviations / multinomial distribution / Poisson distribution / power divergence statistics
© EDP Sciences, SMAI 2020
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