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Simultaneous Test for Independence Among Subvectors of Several Moderately High Dimensional Multivariate Normal Distributions
Dariush Najarzadeh
Abstract:   (611 Views)

‎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.

Keywords: ‎Multivariate Normal Distribution‎, ‎Likelihood Ratio Test‎, ‎High-Dimensional Data‎, Testing Independence‎, ‎Multivariate Gamma Function.
Full-Text [PDF 5088 kb]   (92 Downloads)    
Type of Study: Applied | Subject: Statistical Inference
Received: 2018/01/30 | Accepted: 2018/09/5
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مجله علوم آماری – نشریه علمی پژوهشی انجمن آمار ایران Journal of Statistical Sciences
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