Event Date:
Event Location:
- Psych 1924
Title: The middle-scale asymptotics of Wishart matrices
Abstract:
We study the behavior of a real p-dimensional Wishart random matrix with n degrees of freedom when n,p -> ∞ but p/n -> 0. We establish the existence of phase transitions when p grows at the order n{(K+1)/(K+3)} for every positive integer K, and derive expressions for approximating densities between every two phase transitions. To do this, we make use of a novel tool we call the G-conjugate of an absolutely continuous distribution, which is obtained from the Fourier transform of the square root of its density. I will also discuss applications of the results to high-dimensional inference, asymptotic equivalence of covariance experiments, and random graph theory. This is joint work with Didier Chételat.
Bio:
Martin Wells is the Department Chair and Chales A.Alexander Professor of Statistical Sciences at Cornell University.