B1274
Title: Extreme eigenvalues of sample covariance matrices with generalized elliptical models with applications
Authors: Xiucai Ding - UC Davis (United States) [presenting]
Abstract: The purpose is to present some recent results on the extreme values of the sample covariance matrices where the data matrix is $TXB$; $T$ is a positive definite matrix, and $B$ is a diagonal matrix with i.i.d. random variables independent of $X$. This model is frequently used in statistics. For example, when the columns are uniformly distributed on the unit sphere, the distributed data is elliptical. Another example is when $X$ contains i.i.d. entries, and $B$ contains multinomial or Gaussian random variables, the matrix becomes the standard bootstrapping matrix. It is shown that under different assumptions on $T$ and $B$, the largest singular value of $TXB$ can have five different distributions: Frechet, Gumbel, Weibull, Tracy-Widom, and Gaussian. The innovative approach systematically explores the connection between random matrix theory and classic extreme value theory. Applications in signal detection and bootstrapping will be discussed.
