This paper studies analytic inference along two dimensions of clustering. In such setups, the commonly used approach has two drawbacks. First, the corresponding variance estimator is not necessarily positive. Second, inference is invalid in non-Gaussian regimes, namely when the estimator of the parameter of interest is not asymptotically Gaussian. We consider a simple fix that addresses both issues. In Gaussian regimes, the corresponding tests are asymptotically exact and equivalent to usual ones. Otherwise, the new tests are asymptotically conservative. We also establish their uniform validity over a certain class of data generating processes. Independently of our tests, we highlight potential issues with multiple testing and nonlinear estimators under two-way clustering. Finally, we compare our approach with existing ones through simulations.

翻译：本文研究沿两个聚类维度的解析推断问题。在此类设定中，常用方法存在两个缺陷：首先，对应的方差估计量未必为正定；其次，在非高斯情形（即感兴趣参数的估计量不满足渐近高斯性）下推断无效。我们提出一种能同时解决这两个问题的简易修正方法。在高斯情形中，对应检验具有渐近精确性且与常规检验等价；在其他情形下，新检验具有渐近保守性。我们还在特定数据生成过程类上证明了其一致有效性。独立于检验方法本身，我们揭示了双向聚类框架下多重检验与非线性估计量可能存在的问题。最后通过模拟实验将本方法与现有方法进行对比。