16 Likelihood ratio tests for mean vectors and covariance matrices

Abstract

This chapter describes various likelihood ratio tests on mean vectors and covariance matrices and discusses computations of the critical values associated with these tests. Likelihood ratio tests play an important role in testing various hypotheses under the univariate analysis of variance (ANOVA) and multivariate analysis of variance (MANOVA) models. The chapter discusses the likelihood ratio test for testing for the equality of mean vectors of several multivariate normal populations, the test specifying the mean vector, the distribution of the determinant of the multivariate beta matrix, likelihood ratio test for multiple independence of several sets of variables, the likelihood ratio tests for sphericity and for the multiple homogeneity of the covariance matrices. It also provides likelihood ratio procedure specifying the mean vector and covariance matrix simultaneously, likelihood ratio test for the equality of the mean vectors and the equality of covariance matrices simultaneously, likelihood ratio tests for certain linear structures on the covariance matrices, and the applications of the tests on linear structures in the area of the components of variance.