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Title: BEAUTY powered BEAST Authors:  Kai Zhang - University of North Carolina at Chapel Hill (United States) [presenting]
Zhigen Zhao - Temple University (United States)
Wen Zhou - Colorado State University (United States)
Abstract: Nonparametric dependence detection is studied with the proposed binary expansion approximation of uniformity (BEAUTY) approach, which extends the celebrated Euler's formula, and approximates the characteristic function of any copula distribution with a linear combination of means of binary interactions from marginal binary expansions. This novel theory enables the unification of many important existing tests through an approximation from some quadratic form of symmetry statistics, where the deterministic weight matrix characterizes the power properties of each test. To achieve a robust high power, we study test statistics with data-adaptive weights, referred to as the binary expansion adaptive symmetry test (BEAST). By utilizing the properties of the binary expansion filtration, we show that the Neyman-Pearson test of uniformity can be approximated by an oracle weighted sum of symmetry statistics. The BEAST with this oracle leads all existing tests we considered in empirical power against all forms of alternatives, thus sheds light on the potential of substantial improvements in power and on the form of optimal weights under each alternative. To approach this oracle power, we develop the BEAST through a regularized subsampling approximation of the oracle test. The BEAST improves the empirical power of many existing tests against a wide spectrum of common alternatives while providing a clear interpretation of the form of dependency upon rejection.