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Kernel Ridge Regression Inference
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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.
Forward citations
Cited by 2 Pith papers
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Upper Confidence Bounds for the Prediction Error of Kernel Ridge Regression via Gaussian Refitting
Gaussian-refit movement quantiles plus a bias term give a computable, rate-optimal upper confidence bound on the realized prediction error of kernel ridge regression under symmetric noise.
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Nonparametric Goodness-of-fit Testing under Covariate Shift
Truncated importance-weighted kernel ridge regression with multiplier bootstrap yields valid L2(Q) confidence balls for nonparametric goodness-of-fit under covariate shift.
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