We provide uniform inference and confidence bands for kernel ridge regression (KRR), a widely-used non-parametric regression estimator for general data types including rankings, images, and graphs. Despite the prevalence of these data -- e.g., ranked preference lists in school assignment -- the inferential theory of KRR is not fully known, limiting its role in economics and other scientific domains. We construct sharp, uniform confidence sets for KRR, which shrink at nearly the minimax rate, for general regressors. To conduct inference, we develop an efficient bootstrap procedure that uses symmetrization to cancel bias and limit computational overhead. To justify the procedure, we derive finite-sample, uniform Gaussian and bootstrap couplings for partial sums in a reproducing kernel Hilbert space (RKHS). These imply strong approximation for empirical processes indexed by the RKHS unit ball with logarithmic dependence on the covering number. Simulations verify coverage. We use our procedure to construct a novel test for match effects in school assignment, an important question in education economics with consequences for school choice reforms.

翻译：我们为核岭回归（KRR）提供了均匀推断和置信带方法。核岭回归是一种广泛应用于排名、图像和图等数据类型估计的非参数回归方法。尽管这类数据（如学校分配中的排序偏好列表）普遍存在，但KRR的推断理论尚未完全建立，限制了其在经济学及其他科学领域的应用。我们针对一般回归量构建了以接近极小最大速率收缩的尖锐均匀置信集。为实施推断，我们开发了一种高效的自举程序，通过对称化消除偏差并控制计算开销。为证明该程序的合理性，我们推导了再生核希尔伯特空间（RKHS）中部分和的有限样本均匀高斯耦合与自举耦合。这些结果蕴含了用RKHS单位球索引的经验过程的强逼近，其依赖覆盖数的对数关系。模拟验证了覆盖性能。我们将该程序应用于学校分配中匹配效应的新颖检验——这是教育经济学中影响择校改革的重要问题。