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Abstract:
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We study how to generate a statistical inference procedure that is both computationally efficient and having the theoretical guarantee of its statistical performance. Test of independence plays a fundamental role in many statistical techniques. Among the nonparametric approaches, the distance-based methods (such as the distance correlation based hypotheses testing for independence) have numerous advantages, compared with many other alternatives. A known limitation of the distance-based method is that its computational complexity can be high. In general, when the sample size is n, the order of computational complexity of a distance-based method, which typically requires computing of all pairwise distances, can be O(n^2). Recent advances have discovered that in the univariate cases, a fast method with O(n log n) computational complexity and O(n) memory requirement exists. In this talk, I introduce a test of independence method based on random projection and distance correlation, which achieves nearly the same power as the state-of-the-art distance-based approach, works in the multivariate cases, and enjoys the O(n K log n) computational complexity and O(max{n,K}) memory requirement.
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