Kernel Ridge Regression Inference
This addresses the lack of inferential theory for KRR in applications like school matching, offering a practical tool for researchers and practitioners, though it is incremental in extending existing methods to nonstandard data.
The paper tackles the problem of providing uniform confidence bands for kernel ridge regression (KRR) with nonstandard data, such as preferences and graphs, by constructing valid and sharp confidence sets that shrink at nearly the minimax rate, and applies this to test match effects in school matching.
We provide uniform confidence bands for kernel ridge regression (KRR), a widely used nonparametric regression estimator for nonstandard data such as preferences, sequences, and graphs. Despite the prevalence of these data--e.g., student preferences in school matching mechanisms--the inferential theory of KRR is not fully known. We construct valid and sharp confidence sets that shrink at nearly the minimax rate, allowing nonstandard regressors. Our bootstrap procedure uses anti-symmetric multipliers for computational efficiency and for validity under mis-specification. We use the procedure to develop a test for match effects, i.e. whether students benefit more from the schools they rank highly.