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Abstract:
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Modern statistical applications often involve testing joint independence of a large number of random variables given a relatively small number of samples. To address this, we introduce a class of test statistics for testing joint independence of normal random variables that are based on sums of powers of absolute values of sample correlations. The test statistics are easy to compute in high dimensions, and can be shown to be asymptotically normal as ratios under several different asymptotic regimes, depending on which the power of the sample correlations used. Our results are based on newly derived exact expressions for powers of moments of sample correlations of independent normal random variables. We demonstrate the utility of tests based on this class of test statistics in simulations.
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