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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2021, Vol. 38 ›› Issue (5): 740-750.doi: 10.3969/j.issn.1005-3085.2021.05.013

• • 上一篇    

同参数分布族中多总体一致性的似然比检验（英）

秦永松,   黄梅清   

  1. 广西师范大学统计系，桂林  541004
  • 出版日期:2021-10-15 发布日期:2021-12-15
  • 基金资助:
    国家自然科学基金 (12061017)；广西研究生教育创新基金 (YCSW2021073).

Likelihood Ratio Tests for Homogeneity of Multiple Populations in a Parametric Family

QIN Yongsong,   HUANG Meiqing   

  1. Department of Statistics, Guangxi Normal University, Guilin 541004
  • Online:2021-10-15 Published:2021-12-15
  • Supported by:
    The National Natural Science Foundation of China (12061017); the Innovation Project of Graduate Education in Guangxi Autonomous Region (YCSW2021073).

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摘要：

多个总体一致性的检验是现实中常遇到的问题，已有的结果包括用于正态总体一致性检验的方差分析方法和检验非参数总体一致性的 Kruskal-Wallis 检验，但尚未见参数总体的一致性检验的一般方法．本文构造了同参数分布族多总体一致性检验的似然比统计量，在一定的条件下证明了统计量在零假设下的渐近分布为卡方分布，该结果在一定程度上填补了正态总体的一致性检验的方差分析和非参数总体的一致性检验的 Kruskal-Wallis 检验之间的部分空白．

关键词: 参数族, 一致性检验, 似然比检验

Abstract:

The test for the homogeneity of several populations is a common issue in many application fields. The well-known results related to this issue include the analysis of variance (ANOVA) for normal populations and the Kruskal Wallis Test (KWT) for nonparametric populations, but there is no general result on the test for the homogeneity of parametric populations. In this paper, the likelihood ratio test (LRT) statistic is constructed to test for the homogeneity of several populations which are the members of a parametric family. It is shown that under some regularity conditions and the null hypothesis all distribution functions of the populations are the same, and the limiting distribution of the LRT statistic  is chi-squared distribution. This result fills in a gap between ANOVA for normal populations and KWT for nonparametric populations.

Key words: parametric family, test of homogeneity, likelihood ratio test

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