与多项分布有关的某一类统计量的大偏差的概率

Pub Date : 2020-01-01 DOI:10.1051/ps/2020020

S. Mirakhmedov

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引用次数: 3

摘要

设η = (η1，…，η n)为参数n = η1 +⋯+ η n且pm > 0, m = 1，…，n, p1 +⋯+ pN = 1的多项式随机向量。我们假设N→∞，maxpm→0为N→∞。研究了形式为h1(η1) +⋯+ hN(ηN)的统计量的大偏差概率，其中hm(x)是非负整数值参数的实值函数。作为一般定理的结果，导出了幂散度统计量及其最流行的特殊变体的新的大偏差结果，以及几种计数统计量的大偏差结果。

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

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.

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