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Likelihood ratio tests of correlated multivariate samples
Journal article   Open access   Peer reviewed

Likelihood ratio tests of correlated multivariate samples

Johan Lim, Erning Li and Shin-Jae Lee
Journal of multivariate analysis, Vol.101(3), pp.541-554
2010
DOI: 10.1016/j.jmva.2009.10.011
url
https://doi.org/10.1016/j.jmva.2009.10.011View
Published (Version of record) Open Access

Abstract

We develop methods to compare multiple multivariate normally distributed samples which may be correlated. The methods are new in the context that no assumption is made about the correlations among the samples. Three types of null hypotheses are considered: equality of mean vectors, homogeneity of covariance matrices, and equality of both mean vectors and covariance matrices. We demonstrate that the likelihood ratio test statistics have finite-sample distributions that are functions of two independent Wishart variables and dependent on the covariance matrix of the combined multiple populations. Asymptotic calculations show that the likelihood ratio test statistics converge in distribution to central Chi-squared distributions under the null hypotheses regardless of how the populations are correlated. Following these theoretical findings, we propose a resampling procedure for the implementation of the likelihood ratio tests in which no restrictive assumption is imposed on the structures of the covariance matrices. The empirical size and power of the test procedure are investigated for various sample sizes via simulations. Two examples are provided for illustration. The results show good performance of the methods in terms of test validity and power.
 Correlated samples Empirical rejection probability Equality of mean vectors Homogeneity of covariance matrices Multivariate analysis Resampling

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