Simultaneous Tests for Independence Among Components of Random Vector by Step-Down Multiple Comparison Procedure

In this article, we consider testing independence among components of random vector in multivariate normal population. For testing independence, we use the modified likelihood ratio test statistic which is improved an approximation to χ² distribution of the likelihood ratio test statistic. In order to perform simultaneous tests for independence among components of random vector, we use the step-down multiple comparison procedure based on the closed testing procedure proposed by Marcus et al. (1976 Marcus , R. , Peritz , E. , Gabriel , K. R. ( 1976 ). On closed testing procedures with special reference to ordered analysis of variance . Biometrika 63 : 655 – 660 .Crossref], Web of Science ®] , Google Scholar]). Finally, we perform Monte Carlo simulations and present numerical results.