Nonparametric Goodness-of-fit Testing under Covariate Shift
Zhen Hou, Dong Xia
stat.ME, cs.LG, math.ST, stat.ML
Submitted: 2026-08-05
License: http://creativecommons.org/licenses/by/4.0/
The gist: This paper develops procedures for nonparametric goodness-of-fit testing under covariate shift, where labelled data are drawn from a source population but goodness-of-fit is evaluated for a target
Terminology
Abstract
This paper develops procedures for nonparametric goodness-of-fit testing under covariate shift, where labelled data are drawn from a source population but goodness-of-fit is evaluated for a target population. The distribution mismatch is quantified by either a bounded moment condition or a sub-exponential tail condition on the target-to-source density ratio. Our method combines truncated importance-weighting kernel ridge regression with a multiplier bootstrap to construct confidence sets for the regression function. The truncation stabilizes the importance- weighting kernel ridge regression as well as the bootstrap calibration, making our approach applicable even when the density ratio has heavy tails. We prove nonasymptotic validity and sharpness of the resulting confidence sets under suitable operator compatibility conditions, and establish explicit error rates for coverage probability under specific conditions on the target- to-source density ratio and on the spectral decay of the kernel integral operator. Numerical experiments corroborate our theoretical findings.
Sources
- When is Importance Weighting Correction Needed for Covariate Shift Adaptation?
- Domain Adaptation: Learning Bounds and Algorithms
- Bootstrap Nonparametric Inference under Data Integration
- Kernel Ridge Regression Inference
- Frequentist coverage and sup-norm convergence rate in Gaussian process regression
- Analysis of Kernel Mean Matching under Covariate Shift
- A Minimax Theory of Nonparametric Regression Under Covariate Shift
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