Testing the Hypothesis of independence of a p-variate vector subvectors, as a pretest for many others related tests, is always as a matter of interest. When the sample size n is much larger than the dimension p, the likelihood ratio test (LRT) with chisquare approximation, has an acceptable performance. However, for moderately high-dimensional data by which n is not much larger than p, the chisquare approximation for null distribution of the LRT statistic is no more usable. As a general case, here, a simultaneous subvectors independence testing procedure in all k p-variate normal distributions is considered. To test this hypothesis, a normal approximation for the null distribution of the LRT statistic was proposed. A simulation study was performed to show that the proposed normal approximation outperforms the chisquare approximation. Finally, the proposed testing procedure was applied on prostate cancer data.
Najarzadeh D. Simultaneous Test for Independence Among Subvectors of Several Moderately High Dimensional Multivariate Normal Distributions. JSS 2019; 13 (1) :217-233 URL: http://jss.irstat.ir/article-1-578-en.html