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.
View on arXiv@article{cao2025_2505.06531,
title={ High-Dimensional Importance-Weighted Information Criteria: Theory and Optimality },
author={ Yong-Syun Cao and Shinpei Imori and Ching-Kang Ing },
journal={arXiv preprint arXiv:2505.06531},
year={ 2025 }
}