Detecting Weak Distribution Shifts via Displacement Interpolation
提出一种基于最优传输理论中位移插值的方法，用于检测从零假设分布向备择假设分布的弱系统性偏移，并给出基于Wasserstein距离的假设检验程序，在消费支出和p值异质性两个实证案例中验证了方法有效性。
Detecting weak, systematic distribution shifts and quantitatively modeling individual, heterogeneous responses to policies or incentives have found increasing empirical applications in social and economic sciences. Given two probability distributions P (null) and Q (alternative), we study the problem of detecting weak distribution shift deviating from the null P toward the alternative Q, where the level of deviation vanishes as a function of n, the sample size. We propose a model for weak distribution shifts via displacement interpolation between P and Q, drawing from the optimal transport theory. We study a hypothesis testing procedure based on the Wasserstein distance, derive sharp conditions under which detection is possible, and provide the exact characterization of the asymptotic Type I and Type II errors at the detection boundary using empirical processes. We demonstrate how the proposed testing procedure works in modeling and detecting weak distribution shifts in real datasets using two empirical examples: distribution shifts in consumer spending after COVID-19, and heterogeneity in the published p-values of statistical tests in journals across different disciplines.