Kernel Ridge Regression Inference

TL;DR

This paper develops uniform confidence bands for kernel ridge regression applicable to complex data types, providing valid inference tools and a test for match effects in school choice scenarios.

Contribution

It introduces a new bootstrap-based method for constructing confidence sets in KRR with nonstandard data, achieving near-minimax rates and handling model mis-specification.

Findings

Confidence bands shrink at nearly minimax rate.

Bootstrap procedure is computationally efficient and valid under mis-specification.

Develops a test for assessing match effects in school preferences.

Abstract

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.