XMSE感知的自适应经验贝叶斯估计 / XMSE-Aware Adaptive Empirical Bayes Estimation
1️⃣ 一句话总结
本文提出一种新的混合估计方法,能够在经验贝叶斯收缩和最大似然估计之间自适应切换,当模型假设正确时保留正则化的优势,当模型假设错误时自动退回到稳健的最大似然估计,从而避免传统经验贝叶斯方法因参数假设备受误导而表现更差的问题。
Empirical Bayes (EB) estimators can match the first-order asymptotic risk of maximum likelihood (ML) while behaving very differently at second order: recent excess mean squared error (XMSE) analysis shows that kernel-based EB estimation may be worse than ML when the kernel is poorly aligned with the true parameter. This paper turns that diagnostic into a design principle. We propose an XMSE-aware mixed estimator that interpolates between ML and EB shrinkage. Its fixed-weight XMSE is a scalar quadratic, yielding a closed-form oracle mixing weight that is no worse than both ML and the base EB estimator at the XMSE scale. A plug-in implementation based on finite-sample XMSE approximations is proved consistent, with a second-order oracle regret rate for an interior oracle weight. We further establish a transfer of the regret bound to the fixed-weight risk curve evaluated at the selected weight, a thresholded boundary rule, and extensions to compact kernel families and to finite and growing kernel dictionaries with high-probability oracle bounds. Finite impulse response simulations with SURE-tuned, hard-selection, and trace-corrected baselines, together with the public Silverbox and Cascaded Tanks benchmarks, show that the proposed estimator retains most of the benefit of regularization when it is helpful and retreats toward ML under kernel misspecification, with an identified finite-de analyzed on the benchmarks.
XMSE感知的自适应经验贝叶斯估计 / XMSE-Aware Adaptive Empirical Bayes Estimation
本文提出一种新的混合估计方法,能够在经验贝叶斯收缩和最大似然估计之间自适应切换,当模型假设正确时保留正则化的优势,当模型假设错误时自动退回到稳健的最大似然估计,从而避免传统经验贝叶斯方法因参数假设备受误导而表现更差的问题。
源自 arXiv: 2606.26975