AI 中文总结
本文提出基于方差的异质处理效应检验，聚焦条件平均处理效应方差，针对其标准推断难题，提出内折样本分割算法，经证明该算法能恢复一致性等，模拟显示其规模控制优且功效高，实证应用也检测到传统检验未发现的异质性。
AI 中文摘要
本文针对异质处理效应的存在性提出了一种稳健的非参数假设检验。我们将条件平均处理效应（CATE）的方差作为一个自然的综合参数，非零方差意味着存在相关异质性。对该参数进行标准推断面临理论挑战。一方面，在同一样本上评估方差分量会导致零退化，在同质性原假设下渐近方差趋于零，使标准高斯推断无效。另一方面，通过标准样本分割解耦经验过程会破坏双稳健得分的奈曼正交性。为解决这一挑战，我们提出了一种新颖的内折样本分割算法。通过在相互不相交的子样本上评估方差分量并将它们与相同的折外干扰估计量耦合，我们的方法实现了干扰偏差的代数抵消。我们证明这恢复了一致性和渐近正态性，并确保了第一类错误控制。蒙特卡罗模拟表明，相对于现有检验，所提出的检验在保持高功效的同时实现了更好的规模控制。在对新南威尔士州就业培训计划的实证应用中，该检验检测到了传统非参数检验未能发现的显著异质性。
英文摘要
This paper proposes a robust nonparametric hypothesis test for the existence of heterogeneous treatment effects. We focus on the variance of the Conditional Average Treatment Effect (CATE) as a natural omnibus parameter, where a non-zero variance implies the presence of relevant heterogeneity. Standard inference for this parameter faces a fundamental theoretical challenge. On one hand, evaluating variance components on the same sample leads to null degeneracy, where the asymptotic variance collapses to zero under the null hypothesis of homogeneity, invalidating standard Gaussian inference. On the other hand, decoupling the empirical processes via standard sample-splitting breaks the Neyman orthogonality of the doubly robust scores due to their nonlinear squared loss, which prevents the cancellation of first-order regularization biases. To resolve this challenge, we propose a novel Intra-Fold Sample-Splitting algorithm. By evaluating variance components on mutually disjoint subsamples while coupling them to identical out-of-fold nuisance estimators, our procedure achieves algebraic cancellation of the nuisance biases. We prove this restores consistency and asymptotic normality, and ensures Type I error control. Monte Carlo simulations demonstrate that the proposed test achieves superior size control relative to existing tests while maintaining high power. In an empirical application to the NSW job training program, the test detects significant heterogeneity that traditional nonparametric tests fail to uncover.
