Ridge Regression Under Dense Factor Augmented Models
（密集因子增强模型下的岭回归）
主讲人： Yi He（University of Amsterdam, Netherlands）
主持老师：（北大经院）王法
参与老师：（北大经院）王一鸣、王熙、刘蕴霆
时间：2025年2月28日（周五） 10:00-11:30
地点（线下）：北京大学经济学院107会议室
报告摘要：
This article establishes a comprehensive theory of the optimality, robustness, and cross-validation selection consistency for the ridge regression under factor-augmented models with possibly dense idiosyncratic information. Using spectral analysis for random matrices, we show that the ridge regression is asymptotically efficient in capturing both factor and idiosyncratic information by minimizing the limiting predictive loss among the entire class of spectral regularized estimators under large-dimensional factor models and mixed-effects hypothesis. We derive an asymptotically optimal ridge penalty in closed form and prove that a bias-corrected k-fold cross-validation procedure can adaptively select the best ridge penalty in large samples. We extend the theory to the autoregressive models with many exogenous variables and establish a consistent cross-validation procedure using the what-we-called double ridge regression method. Our results allow for nonparametric distributions for, possibly heavy-tailed, martingale difference errors and idiosyncratic random coefficients and adapt to the cross-sectional and temporal dependence structures of the large-dimensional predictors. We demonstrate the performance of our ridge estimators in simulated examples as well as an economic dataset. All the proofs are available in the supplementary materials, which also includes more technical discussions and remarks, extra simulation results, and useful lemmas that may be of independent interest.
主讲人简介：
Yi He is an Associate Professor in the Quantitative Economics Section at the University of Amsterdam. He earned his master's degree from the University of Cambridge and his PhD from Tilburg University in 2016. Before returning to the Netherlands, he served as a tenured Assistant Professor in the Department of Econometrics and Business Statistics at Monash University in Australia. His research focuses on high-dimensional econometrics, random matrix theory, extreme value statistics, bootstrapping, and machine learning. His work has been featured in prestigious journals, including the Journal of the American Statistical Association, The Annals of Statistics, Journal of the Royal Statistical Society - Series B, Journal of Business & Economic Statistics, and Journal of Econometrics. Yi's breakthroughs in extreme value statistics have earned him a nomination for the 2025 Van Dantzig Award in Statistics and Operations Research in the Netherlands. His current research explores dense time series models with complex network interactions in high-dimensional econometrics.
