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：本研究探讨了双向聚类数据下线性分位数回归的统计推断问题。基于独立可交换阵列框架与分位数得分函数的投影分解，我们刻画了不同机制下的收敛速率并建立了自归一化高斯逼近。我们提出了一种双向聚类稳健的三明治方差估计量，该估计量采用基于核函数的密度"面包矩阵"与投影匹配的"肉矩阵"，并在高斯机制下证明了其一致性与推断有效性。同时，我们在非高斯交互机制中证明了均匀推断的不可能性结果。