14:00 – 15:00 –Andrew McCormack (Technical University of Munich)

Title: Information Geometry and Asymptotics for Kronecker Covariances

Abstract: The Kronecker covariance structure for array data posits that the covariances along comparable modes, such as rows and columns, of an array are similar. Over and above being a plausible model for many types of data, the Kronecker covariance assumption is especially useful in high-dimensional settings, where unconstrained covariance matrix estimates are often unstable. In this talk we explore asymptotics and information geometric aspects of estimators of Kronecker covariance matrices. The asymptotic properties of two estimators, the maximum likelihood estimator and an estimator based on partial traces are compared. It is shown that the partial trace estimator is inefficient, where the relative performance of this estimator can be quantified in terms of a principle angle between tangent spaces. We also discuss a consistency property of the partial trace estimator and demonstrate that for higher-order tensors the covariance matrix can be consistently estimated in a fixed-n and large-p regime.

Refreshments available between 15:00 – 15:30, Huxley Common Room (HXLY 549)