Title: On high-dimensional robust regression and the bootstrap
Authors: Noureddine El Karoui - UC Berkeley (United States) [presenting]
Abstract: Recent work will be discussed on high-dimensional robust regression and the bootstrap. Very interestingly, ideas connected to the analysis of robust regression estimators in high-dimension gives insight into the performance of the bootstrap. A number of surprising results will be discussed, including the fact that two equally intuitive (in low-dimension) bootstraps perform very differently in high-dimension: one leads to extremely conservative confidence intervals, the other to anti-conservative confidence intervals. Furthermore, it can be shown that maximum likelihood methods for high-dimensional regression lead to inefficient estimators. More problems with the bootstrap in moderate to high-dimension will be discussed. Generically, it seems that the bootstrap does not give statistically valid inferential statements in this context, even when it does in its low-dimensional counterparts.