多参数总体一致性的似然比检验

发布时间：2018-03-24 13:37

本文选题：参数族　切入点：一致性检验　出处：《广西师范大学》2017年硕士论文

【摘要】：参数似然比检验是由Neyman-Pearson在1928年提出来的一种参数检验方法,其基本思路是依据Fisher提出的似然原理得到拒绝域.在总体参数分布族已知的情形下,该检验往往优于非参数检验.为了研究同一参数族下多个总体的一致性检验问题,本文定义了一种参数似然比函数,证明相应的参数似然比统计量在原假设为真时在一定的正则条件下的渐近分布是标准卡方分布,并据此给出了同一参数族下多总体一致性的检验方法.本文主要分为三章:第一章为绪论,简单介绍似然比检验的概念及似然比检验的研究概况,Kruskal-Wallis检验法(KWT)的概念及研究概况,及本文的主要研究内容和主要结果及创新点.第二章将构造似然比检验(LRT)统计量去解决假设检验问题,结果表明:当原假设为真时在一定的正则条件下,似然比检验(LRT)统计量的极限分布为χs2(k-1).并给出本文的一些假设条件和主要结果,模拟结果,引理及主要结果的证明.本文的创新性体现在以下两个方面:1、在同一分布族的条件下,应用似然比检验的方法来判断各组样本是否来自同一分布,即一致性检验,结果表明,所得到的似然比检验统计量的渐近分布为标准卡方分布.2、通过数值模拟,发现,LRT的模拟结果要优于KWT的模拟结果.
[Abstract]:The parameter likelihood ratio test is a parameter test method proposed by Neyman-Pearson in 1928. Its basic idea is to obtain the rejection domain according to the likelihood principle proposed by Fisher. This test is usually superior to the nonparametric test. In order to study the consistency test of multiple populations under the same parameter family, a parameter likelihood ratio function is defined in this paper. It is proved that the asymptotic distribution of the corresponding parameter likelihood ratio statistic is a standard chi-square distribution under certain regular conditions if the original assumption is true. Based on this, the test method of multi-population consistency under the same parameter family is given. This paper is divided into three chapters: the first chapter is an introduction, which briefly introduces the concept of likelihood ratio test and the research survey of likelihood ratio test and the concept and research survey of Kruskal-Wallis test. In the second chapter, we will construct likelihood ratio test (LRT) statistics to solve the hypothesis test problem. The results show that: when the original hypothesis is true, under certain regular conditions, The limit distribution of likelihood ratio test (LRT) statistic is 蠂 S2 / K ~ (-1). Some hypotheses and main results, simulation results, Lemma and proof of main results are given in this paper. The innovation of this paper is embodied in the following two aspects: 1, under the condition of the same distribution family, The method of likelihood ratio test is used to judge whether each group of samples comes from the same distribution, that is, consistency test. The result shows that the asymptotic distribution of the likelihood ratio test statistic is standard chi-square distribution. It is found that the simulation results of LRT are better than those of KWT.
【学位授予单位】：广西师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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