BEAUTY 驱动的 BEAST
BEAUTY Powered BEAST
AI总结：
本文提出 BEAUTY 方法统一近似 copula 特征函数，并基于数据自适应权重设计 BEAST 检验，通过正则化重采样逼近 oracle 功效，在多种备择假设下提升拟合优度检验功效并解释依赖形式。
摘要：
我们利用所提出的均匀性二元展开近似（BEAUTY）方法研究无分布拟合优度检验。该方法推广了著名的欧拉公式，并通过边缘二元展开中二元交互期望的线性组合来近似任意 copula 的特征函数。这一新理论使得许多重要的独立性检验能够通过对称统计量特定二次型的近似得到统一，其中确定性权重矩阵刻画了每个检验的功效性质。为了实现稳健的功效，我们考察具有数据自适应权重的检验统计量，称之为二元展开自适应对称检验（BEAST）。对于任意给定的备择假设，我们证明 Neyman-Pearson 检验可以由对称统计量的一个 oracle 加权和来近似。带有该 oracle 的 BEAST 为可行功效提供了一个有用的基准。为接近这一 oracle 功效，我们通过对 oracle 检验进行正则化重采样近似来设计 BEAST。BEAST 在广泛的常见备择假设下提升了许多现有检验的经验功效，并在显著时对依赖形式给出了清晰的解释。
英文摘要：
We study distribution-free goodness-of-fit tests with the proposed Binary Expansion Approximation of UniformiTY (BEAUTY) approach. This method generalizes the renowned Euler's formula, and approximates the characteristic function of any copula through a linear combination of expectations of binary interactions from marginal binary expansions. This novel theory enables a unification of many important tests of independence via approximations from specific quadratic forms of symmetry statistics, where the deterministic weight matrix characterizes the power properties of each test. To achieve a robust power, we examine test statistics with data-adaptive weights, referred to as the Binary Expansion Adaptive Symmetry Test (BEAST). For any given alternative, we demonstrate that the Neyman-Pearson test can be approximated by an oracle weighted sum of symmetry statistics. The BEAST with this oracle provides a useful benchmark of feasible power. To approach this oracle power, we devise 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 and delivers a clear interpretation of dependency forms when significant.
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