使用交叉验证后再自助法选择高维M-估计量的惩罚参数
Selecting Penalty Parameters of High-Dimensional M-Estimators using Bootstrapping after Cross-Validation
AI总结：
提出交叉验证后再自助法为高维$\ell_1$-惩罚M-估计量选择惩罚参数，推导了估计量收敛速度，并通过模拟与实证证明其在推断上优于交叉验证。
摘要：
我们提出了一种在高维情况下为$\ell_{1}$-惩罚M-估计量选择惩罚参数的新方法，我们称之为交叉验证后再自助法。我们推导了相应的$\ell_1$-惩罚M-估计量以及后$\ell_1$-惩罚M-估计量的收敛速度，后者在准则函数中不加惩罚地重新拟合前一估计量的非零项。我们通过模拟证明，我们的方法在估计误差方面不被交叉验证所支配，并且在推断方面可以优于交叉验证。作为实证说明，我们重新审视了Fryer Jr (2019)，他调查了警察使用武力的种族差异，并证实了他的发现。
英文摘要：
We develop a new method for selecting the penalty parameter for $\ell_{1}$-penalized M-estimators in high dimensions, which we refer to as bootstrapping after cross-validation. We derive rates of convergence for the corresponding $\ell_1$-penalized M-estimator and also for the post-$\ell_1$-penalized M-estimator, which refits the non-zero entries of the former estimator without penalty in the criterion function. We demonstrate via simulations that our methods are not dominated by cross-validation in terms of estimation errors and can outperform cross-validation in terms of inference. As an empirical illustration, we revisit Fryer Jr (2019), who investigated racial differences in police use of force, and confirm his findings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
