Bootstrap Nonparametric Inference Under Data Integration

ABSTRACT We propose multiplier bootstrap procedures for nonparametric inference and uncertainty quantification of the target mean function, based on a framework of integrating target and source data under a covariate shift scenario with equal target and source mean functions. We propose estimation and inferential procedures through a straightforward combination of all target and source datasets. Our method enables local and global inference on the target mean function without using asymptotic distributions. To justify our approach, we derive an optimal convergence rate for the nonparametric estimator and establish bootstrap consistency to estimate the asymptotic distribution of the nonparametric estimator. The proof of global bootstrap consistency involves a central limit theorem for quadratic forms with dependent variables under a conditional probability measure.