🤖 AI Summary
This study addresses the challenge of statistical inference for quantile regression in two-way clustered data with complex dependence structures. The authors propose a robust sandwich variance estimator grounded in the framework of exchangeable arrays and a decomposition of quantile score projections: the "bread" component is constructed via kernel density estimation, while the "meat" component is built through projection matching. Building on this estimator, they develop a self-normalized Gaussian approximation theory, establishing its consistency and valid inferential properties under Gaussian interaction regimes. They further demonstrate the impossibility of consistent inference in non-Gaussian settings. Theoretical analysis reveals that the convergence rate is jointly determined by the two-way clustering structure.
📝 Abstract
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.