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

Abstract

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). Finally, we perform Monte Carlo simulations and present numerical results.

Keywords:

• Closed testing procedure
• Modified likelihood ratio
• Step-down multiple comparison procedure
• Testing independence

2000 Mathematics Subject Classification:

• Primary 62H15
• Secondary 62H10

Acknowledgments

The authors would like to express their sincere gratitude to Professor Tsunehisa Imada of Tokai University for his useful comments. The authors would also like to thank to the referee for his helpful advices and comments. The research of the second author was supported in part by Grant-in-Aid for Young Scientists (B) under Contract Number 21700311.