Abstract:
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Testing independence among a number of (ultra) high-dimensional random samples is an fundamental and challenging problem. By arranging n identically distributed p-dimensional random vectors into a p by n data matrix, we investigate the testing problem on independence among columns under the matrix-variate normal modeling of the data. We propose a computationally simple and tuning free test statistic, characterize its limiting null distribution, analyze the statistical power and prove its minimax optimality. As an important by-product of the test statistic, a ratio-consistent estimator for the quadratic functional of covariance matrix from correlated samples is developed.
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