Speaker: Jing Lei

Abstract: I will lead the discussion of the paper on high-dimensional bootstrap by El Karoui and Purdom. The paper studies two variants of the bootstrap in linear regression models with 0 < p/n < 1 using ERM estimators with convex loss functions. I will mostly cover the first variant: the residual bootstrap. The key technical component is a dual leave-one-out analysis that characterizes the behavior of the fitted residuals and the estimation error, which is the main contribution of the earlier work by El Karoui and Co.