Multiplier bootstrap procedures for local and global inference on a target mean function when limited target data are integrated with larger source datasets. Under covariate shift the datasets are pooled directly into a weighted kernel ridge regression; under general distribution shift a two-step procedure first estimates target-to-source mean differences on held-out portions, adjusts the remaining source data, and then bootstraps the combined sample. The theory delivers an optimal convergence rate for the integrated estimator and bootstrap consistency, with global consistency resting on a central limit theorem for quadratic forms with dependent variables under a conditional measure.
We propose multiplier bootstrap procedures for nonparametric inference and uncertainty quantification of the target mean function, based on a novel framework of integrating target and source data. We…