序贯抽样数据中的假设检验：最大化超越独立同分布抽样功效的 AdapRT
Hypothesis Testing in Sequentially Sampled Data: AdapRT to Maximize Power Beyond iid Sampling
AI总结：
提出自适应随机化检验（ART）方法，允许数据自适应抽样以解决变量独立性问题，理论证明其在多臂老虎机与联合分析中功效超越传统独立同分布抽样的CRT。
摘要：
检验感兴趣的变量是否影响结果是统计学中最基本的问题之一，也常常是主要的科学关注点。为解决此问题，条件随机化检验（CRT）被广泛用于在保持其他变量（Z）固定的情况下，检验感兴趣的变量（X）与结果（Y）的独立性。CRT 使用随机化或基于设计的推断，仅依赖于 (X,Z) 的独立同分布（iid）抽样来生成使用任何检验统计量构建的精确有限样本 p 值。我们提出了一种新方法，即自适应随机化检验（ART），该方法在允许数据被自适应抽样的同时解决独立性问题。我们首先在一个被称为正态均值模型的特定多臂老虎机问题中展示 ART。在此设置下，我们从理论上刻画了独立同分布抽样过程和自适应抽样过程的功效，并实证发现 ART 能够一致地优于以相等概率独立拉动所有臂的 CRT。令人惊讶的是，我们还发现当信号相对较强时，ART 的功效甚至能超过使用预言机独立同分布抽样过程的 CRT。我们认为，所提出的自适应过程之所以成功，是因为它能够提取那些由于随机机会最初看起来像“虚假”信号的臂，并将其稳定得更接近“零”信号。此外，我们还将 ART 应用于一种被称为联合分析的流行因子调查设计设置中。通过模拟以及一项关于性别歧视在政治候选人评价中作用的最新应用，我们发现了类似的结果。
英文摘要：
Testing whether a variable of interest affects the outcome is one of the most fundamental problem in statistics and is often the main scientific question of interest. To tackle this problem, the conditional randomization test (CRT) is widely used to test the independence of variable(s) of interest (X) with an outcome (Y) holding other variable(s) (Z) fixed. The CRT uses randomization or design-based inference that relies solely on the iid sampling of (X,Z) to produce exact finite-sample p-values that are constructed using any test statistic. We propose a new method, the adaptive randomization test (ART), that tackles the independence problem while allowing the data to be adaptively sampled. We first showcase the ART in a particular multi-arm bandit problem known as the normal-mean model. Under this setting, we theoretically characterize the powers of both the iid sampling procedure and the adaptive sampling procedure and empirically find that the ART can uniformly outperform the CRT that pulls all arms independently with equal probability. We also surprisingly find that the ART can be more powerful than even the CRT that uses an oracle iid sampling procedure when the signal is relatively strong. We believe that the proposed adaptive procedure is successful because it takes arms that may initially look like "fake" signals due to random chance and stabilizes them closer to "null" signals. We additionally showcase the ART to a popular factorial survey design setting known as conjoint analysis. We find similar results through simulations and a recent application concerning the role of gender discrimination in political candidate evaluation.
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