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 in terms of so called -intermediate asymptotic efficiency due to Ivchenko and Mirakhmedov (1995), 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.
翻译:研究的主题是对多种分布的统一性进行测试的问题。我们考虑基于对称统计的测试,定义为细胞分布的某些功能之和。主要关注的焦点是权力差异统计类别,特别是基平方和日志相似性比率统计。文章的主要问题是研究测试在中间环境概念中的无症状特性,即因Ivchenko和Mirakhmedov(1995年)而出现的所谓中间无症状效率,因为当时试验的无症状能力与零和一相隔开来,而替代方法的顺序与假设一致,但不会太快。