We study inference for linear quantile regression with two-way clustered data. Using a separately exchangeable array framework and a projection decomposition of the quantile score, we characterize regime-dependent convergence rates and establish a self-normalized Gaussian approximation. We propose a two-way cluster-robust sandwich variance estimator with a kernel-based density ``bread'' and a projection-matched ``meat'', and prove consistency and validity of inference in Gaussian regimes. We also show an impossibility result for uniform inference in a non-Gaussian interaction regime.

翻译：我们研究了具有双向聚类数据的线性分位数回归的推断问题。利用可分离交换数组框架和分位数得分的投影分解，我们刻画了依赖于机制的收敛速度，并建立了自归一化高斯近似。我们提出了一种双向聚类稳健三明治方差估计量，其“面包”部分基于核密度估计，“肉”部分与投影匹配，并证明了在高斯机制下推断的一致性和有效性。我们还展示了在非高斯交互机制下无法进行均匀推断的不可行性结果。