Mathematics Seminar - Dr. Johannes Heiny

Title: Extremes of functions of high-dimensional random vectors with applications in statistics

Abstract:

High-dimensional data play an important role in many fields of modern sciences. In this talk, we study extremes of functions of high-dimensional random vectors with a particular focus on applications in statistics and geometry. We derive the asymptotic distribution of the largest interpoint distance of high-dimensional random points and deduce a testing procedure for the change-point in their means. We will also discuss an extension to point processes and properties of the eigenvalues of sample correlation matrices when the number of random vectors and their dimension tend to infinity.