On the intermediate asymptotic efficiency of goodness-of-fit tests in multinomial distributions

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Esaim-Probability and Statistics Pub Date : 2022-08-24 DOI:10.1051/ps/2022010

S. Mirakhmedov

引用次数: 2

Abstract

We consider goodness-of-fit tests for uniformity of a multinomial distribution by means of tests based on a class of symmetric statistics, defined as the sum of some function of cell-frequencies. We are dealing with an asymptotic regime, where the number of cells grows with the sample size. Most attention is focused on the class of power divergence statistics. The aim of this article is to study the intermediate asymptotic relative efficiency of two tests, where the powers of the tests are asymptotically non-degenerate and the sequences of alternatives converge to the hypothesis, but not too fast. The intermediate asymptotic relative efficiency of the chi-square test wrt an arbitrary symmetric test is considered in details.

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多项分布中拟合优度检验的中间渐近效率

本文通过基于一类对称统计量的检验来考虑多项分布均匀性的拟合优度检验，这些统计量被定义为一些细胞频率函数的和。我们正在处理一个渐近状态，其中细胞的数量随着样本量的增加而增加。人们最关注的是功率发散统计类。本文的目的是研究两个检验的中间渐近相对效率，其中检验的幂是渐近非退化的，并且备选序列收敛于假设，但不是太快。详细讨论了卡方检验对任意对称检验的中间渐近相对效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Esaim-Probability and Statistics STATISTICS & PROBABILITY-

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains. Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics. Long papers are very welcome. Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.