DMS Statistics and Data Science Seminar

Speaker: Miles Lopes (UC Davis)

Title: Rates of Approximation for CLT and Bootstrap in High Dimensions

Abstract: In the setting of low-dimensional data, it is well known that the distribution of a sample mean can be consistently approximated using the CLT or bootstrap methods. Also, the classical Berry-Esseen theorem shows that such approximations can achieve a rate of order n^{-1/2}, where accuracy is measured with respect to the "Kolmogorov distance." However, until recently, it was an open problem to determine if Berry-Esseen type bounds with near n^{-1/2} rates can be established in the context of high-dimensional data --- which stimulated many advances in the literature during the last several years. ln this talk, I will survey these developments and discuss some of my own work on this problem.