Nonparametric Goodness-of-fit Testing under Covariate Shift
This paper studies nonparametric goodness-of-fit testing when labeled data come from a source population but evaluation concerns a target population under covariate shift. It combines truncated importance-weighted kernel ridge regression with a multiplier bootstrap to construct confidence sets for the regression function. Truncation is designed to stabilize both estimation and bootstrap calibration, including settings with heavy-tailed target-to-source density ratios. Under operator compatibility conditions, the authors establish nonasymptotic validity and sharpness, with explicit coverage-error rates tied to density-ratio assumptions and spectral decay of the kernel operator. Numerical experiments are reported as supporting evidence.
Why it's worth reading
Covariate shift can invalidate ordinary regression checks for the deployment population. This work is timely because it offers a theoretically calibrated approach that explicitly handles unstable or heavy-tailed density ratios through truncation.