Likelihood Ratio Tests For Homogeneity Of Multiple Populations Under General Parametric Families

The parametric likelihood ratio test,which proposed by Neyman and Pearson in 1928,is a kind of important method of parametric test.Of which the main idea is to obtain the rejection region based on the Fisher's likelihood principle of.When the general parameter distribution family is known to us,the test takes advantage over the nonparametric tests.In order to study the problem of homogeneity test with the same overall parameter family of multiple parameters,this paper defines a likelihood ratio test(LRT),proves that the LRT is asymptotically distributed as chi-squared distribution,and then presents the LRT method to test the homogeneity of multiple populations under general parametric families.This thesis contains three chapters:The first chapter is introduction.We introduce the concept of the likelihood ratio test and the research situation of likelihood ratio test,the definition of Kruskal-Wallis test(KWT)and the research situation,the main research contents and innovation points in this thesis.The second chapter constructs the likelihood ratio test(LRT)statistic to solve the problem of hypothesis test.It is shown,under some regularity conditions and under the null hypothesis that the limiting distribution of the LRT is chi-squared distribution.And we give some assumptions and main results,simulation results,some lemmas and the proof of the main results.The innovation of this thesis is mainly reflected in the following two aspects:1.Under the condition of the same distribution family,the application of the likelihood ratio test method to determine whether each sample from the same distribution,namely test of homo-geneity,is investigated.The results show that the likelihood ratio test obtained has the asymptotic distribution of chi-squared distribution.2.Through numerical simulation,it is shown that the simulation results of LRT in this paper are better than that of KWT.