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.
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DOI : 10.1051/ps/2020020
Keywords: Chi-square statistic, count statistics, log-likelihood ration statistic, large deviations, multinomial distribution, Poisson distribution, power divergence statistics
@article{PS_2020__24_1_581_0,
author = {Mirakhmedov, Sherzod M.},
title = {The probabilities of large deviations for a certain class of statistics associated with multinomial distribution},
journal = {ESAIM: Probability and Statistics},
pages = {581--606},
year = {2020},
publisher = {EDP Sciences},
volume = {24},
doi = {10.1051/ps/2020020},
mrnumber = {4160332},
zbl = {1455.60046},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2020020/}
}
TY - JOUR AU - Mirakhmedov, Sherzod M. TI - The probabilities of large deviations for a certain class of statistics associated with multinomial distribution JO - ESAIM: Probability and Statistics PY - 2020 SP - 581 EP - 606 VL - 24 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ps/2020020/ DO - 10.1051/ps/2020020 LA - en ID - PS_2020__24_1_581_0 ER -
%0 Journal Article %A Mirakhmedov, Sherzod M. %T The probabilities of large deviations for a certain class of statistics associated with multinomial distribution %J ESAIM: Probability and Statistics %D 2020 %P 581-606 %V 24 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ps/2020020/ %R 10.1051/ps/2020020 %G en %F PS_2020__24_1_581_0
Mirakhmedov, Sherzod M. The probabilities of large deviations for a certain class of statistics associated with multinomial distribution. ESAIM: Probability and Statistics, Tome 24 (2020), pp. 581-606. doi: 10.1051/ps/2020020
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