Randomization Tests Under an Approximate Symmetry Assumption
发展了近似对称假设下的随机化检验理论，允许数据在聚类内和聚类间存在异质性和依赖，适用于有限个聚类、每个聚类内大量观测的场景，并在模拟和实证中展示了优势。
This paper develops a theory of randomization tests under an approximate symmetry assumption. Randomization tests provide a general means of constructing tests that control size in nite samples whenever the distribution of the observed data exhibits symmetry under the null hypothesis. Here, by exhibits symmetry we mean that the distribution remains invariant under a group of transformations. In this paper, we provide conditions under which the same construction can be used to construct tests that asymptotically control the probability of a false rejection whenever the distribution of the observed data exhibits approximate symmetry in the sense that the limiting distribution of a function of the data exhibits symmetry under the null hypothesis. An important application of this idea is in settings where the data may be grouped into a xed number of \clusters with a large number of observations within each cluster. In such settings, we show that the distribution of the observed data satises our approximate symmetry requirement under weak assumptions. In particular, our results allow for the clusters to be heterogeneous and also have dependence not only within each cluster, but also across clusters. This approach enjoys several advantages over other approaches in these settings. Among other things, it leads to a test that is asymptotically similar, which, as shown in a simulation study, translates into improved power at many alternatives. Finally, we use our results to revisit the analysis of Angrist and Lavy (2009), who examine the impact of a cash award on exam performance for low-achievement students in Israel.