标题： 序列采样数据中的假设检验：AdapRT在独立同分布采样之外最大化功效 显示英文标题

标题： Hypothesis Testing in Sequentially Sampled Data: AdapRT to Maximize Power Beyond iid Sampling

摘要： 测试一个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。 为了处理这个问题，条件随机化检验（CRT）是一种基于设计的方法，广泛用于在固定一些控制变量（Z）的情况下测试一个感兴趣的变量（X）与结果（Y）的独立性。 CRT仅依赖于（X,Z）的随机独立同分布抽样，以产生精确的小样本p值，这些p值可以使用任何检验统计量构建。 我们提出了一种新方法，自适应随机化检验（AdapRT），它同样处理独立性问题，但允许数据依次抽样。 与CRT类似，AdapRT仅依赖于了解（X,Z）的（自适应）抽样分布。 在本文中，我们还展示了在两个示例设置中通过自适应抽样显著提高的统计功效。 我们首先在一个称为正态均值模型的多臂老虎机问题中展示AdapRT。 在这一设定下，我们理论上描述了独立同分布抽样方案和AdapRT的功效，并通过实证发现AdapRT可以始终优于典型的均匀独立同分布抽样方案，该方案以相等的概率拉动所有臂。 我们还意外地发现，当信号相对较强时，AdapRT甚至比理想的独立同分布抽样方案更有效。 我们认为，所提出的自适应过程成功的主要原因是它稳定了最初看起来像“虚假”信号的臂。 我们还将AdapRT应用于一种流行的因子调查设计设置，即联合分析，并通过模拟和应用发现了类似的结果。 最后，我们还为从业者提供了一个功效分析流程，以诊断其提出的自适应过程的有效性，并将该流程应用于上述两个设置。 显示英文摘要

摘要： Testing whether a variable of interest affects the outcome is one of the most fundamental problems in statistics. To tackle this problem, the conditional randomization test (CRT) is a design-based method that is widely used to test the independence of a variable of interest (X) with an outcome (Y) holding some controls (Z) fixed. The CRT relies solely on the random 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 (AdapRT), that similarly tackles the independence problem but allows the data to be sequentially sampled. Like the CRT, the AdapRT relies solely on knowing the (adaptive) sampling distribution of (X,Z). In this paper, we additionally show the significant power increase by adaptively sampling in two illustrative settings. We first showcase the AdapRT 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 scheme and the AdapRT and empirically find that the AdapRT can uniformly outperform the typical uniform iid sampling scheme that pulls all arms with equal probability. We also surprisingly find that the AdapRT can be more powerful than even the oracle iid sampling scheme when the signal is relatively strong. We believe that the proposed adaptive procedure is successful mainly because it stabilizes arms that may initially look like "fake" signal. We additionally showcase the AdapRT to a popular factorial survey design setting known as conjoint analysis and find similar results through both simulations and application. Lastly, we also provide a power analysis pipeline for practitioners to diagnosis the effectiveness of their proposed adaptive procedures and apply the pipeline to the two aforementioned settings.