CMSA Talk: Noureddine El Karoui

Title: Some Remarks on the Bootstrap in High-Dimension Abstract: The bootstrap (Efron, 79) is a ubiquitous tool in applied statistics. The bootstrap seeks to address the following central question: is it possible to understand the fluctuation behavior of certain functions of the data by appropriately sampling from the observed dataset? (This question is of course important if one wants to create confidence intervals/error bars for functions of the data of interest to the data analyst without relying on asymptotic analysis.) After reviewing some classical results in the situation where one works with data whom dimension, p, is much smaller than the number of observations, n, I will discuss some results concerning the high-dimensional situation where p and n are of the same order of magnitude. As we will see, numerous issues arise in this setting, casting some doubts about the reliability of the bootstrap in high-dimension. No familiarity with resampling methods will be assumed. Based on joint work with Elizabeth Purdom. (Special Seminar: flyer)