The paper proves nonasymptotic coverage guarantees for bootstrap confidence balls around a truncated importance-weighted kernel ridge estimator in the target L2 metric under covariate shift.
High-Dimensional Importance-Weighted Information Criteria: Theory and Optimality
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abstract
Imori and Ing (2025) proposed the importance-weighted orthogonal greedy algorithm (IWOGA) for model selection in high-dimensional misspecified regression models under covariate shift. To determine the number of IWOGA iterations, they introduced the high-dimensional importance-weighted information criterion (HDIWIC). They argued that the combined use of IWOGA and HDIWIC, IWOGA + HDIWIC, achieves an optimal trade-off between variance and squared bias, leading to optimal convergence rates in terms of conditional mean squared prediction error. In this article, we provide a theoretical justification for this claim by establishing the optimality of IWOGA + HDIWIC under a set of reasonable assumptions.
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Nonparametric Goodness-of-fit Testing under Covariate Shift
The paper proves nonasymptotic coverage guarantees for bootstrap confidence balls around a truncated importance-weighted kernel ridge estimator in the target L2 metric under covariate shift.