Seminar - Martin Wells

Event Date: 

Wednesday, February 20, 2019 - 3:30pm

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.

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