Abstract

The object of study is the problem of testing for uniformity of the multinomial distribution. We consider tests based on symmetric statistics, defined as the sum of some function of cell-frequencies. Mainly, attention is focused on the class of power divergence statistics, in particular, on the chi-square and log-likelihood ratio statistics. The main issue of the article is to study the asymptotic properties of tests at the concept of an intermediate setting, when the asymptotic power of tests are bounded away from zero and one, while sequences of alternatives converge to the hypothesis, but not too fast.

中文翻译：

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某类多项式分布拟合优度检验的渐近性质

摘要

研究对象是检验多项式分布的均匀性问题。我们考虑基于对称统计的测试，定义为细胞频率的某些函数的总和。主要关注幂散度统计类，特别是卡方和对数似然比统计。本文的主要问题是在中间设置的概念下研究测试的渐近特性，当测试的渐近能力远离 0 和 1 时，备选方案序列收敛到假设，但不会太快。