Selecting Penalty Parameters of High-Dimensional M-Estimators Using Bootstrapping after Cross Validation

• 成果类型: Article
• 署名作者: Chetverikov, Denis; Sorensen, Jesper Riis-Vestergaard
• 署名单位: University of California System; University of California Los Angeles; University of Copenhagen
• 刊物名称: JOURNAL OF POLITICAL ECONOMY
• ISSN/ISSBN: 0022-3808
• DOI: 10.1086/736770
• 发表日期: 2025
• 页码: 3208-3248
• 关键词: GENERALIZED LINEAR-MODELS; least-squares estimation; quantile regression; DANTZIG SELECTOR; Lasso

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 nonzero 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 (2019), who investigated racial differences in police use of force, and confirm his findings.