beauty有权力的东亚 (BEAUTY Powered BEAST)

We study nonparametric dependence detection with the proposed binary expansion approximation of uniformity (BEAUTY) approach, which generalizes the celebrated Euler's formula, and approximates the characteristic function of any copula with a linear combination of expectations of binary interactions from marginal binary expansions. This novel theory enables a unification of many important tests through approximations from some quadratic forms of symmetry statistics, where the deterministic weight matrix characterizes the power properties of each test. To achieve a robust 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 provides a benchmark of feasible power against any alternative by leading all existing tests with a substantial margin. To approach this oracle power, we develop the BEAST through a regularized resampling approximation of the oracle test. The BEAST improves the empirical power of many existing tests against a wide spectrum of common alternatives while providing clear interpretation of the form of dependency upon rejection.

翻译：我们研究非对称依赖性检测,采用拟议的统一(BEAUTY)二进制扩展近似法(BEAUTY)方法,该方法将已知的Euler的公式概括为通用,并近似任何相交合体的特征功能,同时将边际二进制扩张的二进制互动期望线性结合为线性组合。这个新颖的理论使得许多重要测试能够通过某些对称统计的四进制形式的近似值统一起来,其中确定性重量矩阵代表了每项测试的功率特性。为了实现强力,我们研究以数据适应性重量来测试统计数据,称为二进制适应性适应性对称测试(BEARTS)。我们利用二进制扩张过滤法的特性,我们表明,对统一的奈曼-皮尔森测试可以通过对对正对称性统计的某一或极重的加权总和来进行准。用这个或极分导所有现有测试,为可行的功率提供了基准。为了达到这一功率,我们通过对质性调整的二进制扩展的替代体测试,我们通过常规的复选近近度测试(BEAST)来开发BEASTRTst),同时提供对常规的常规的普通的试测测测测测测度,同时对普通的试。