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Testing for complete independence in high dimensions. (English) Zbl 1151.62327

Summary: A simple statistic is proposed for testing the complete independence of random variables having a multivariate normal distribution. The asymptotic null distribution of this statistic, as both the sample size and the number of variables go to infinity, is shown to be normal. Consequently, this test can be used when the number of variables is not small relative to the sample size and, in particular, even when the number of variables exceeds the sample size. The finite sample size performance of the normal approximation is evaluated in a simulation study and the results are compared to those of the likelihood ratio test.

MSC:

62H15 Hypothesis testing in multivariate analysis
62E20 Asymptotic distribution theory in statistics
65C60 Computational problems in statistics (MSC2010)
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