B1234
Title: Entropic covariance models
Authors: Piotr Zwiernik - University of Toronto (Canada) [presenting]
Abstract: In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance matrix or its inverse. Another approach considers linear restrictions on the matrix logarithm of the covariance matrix. A general framework for linear restrictions is presented on different transformations of the covariance matrix, including the mentioned examples. The proposed estimation method solves a convex problem and yields an M-estimator, allowing for relatively straightforward asymptotic and finite sample analysis. After developing the general theory, modelling correlation matrices and sparsity are analyzed. The geometric insights enable the extension of various recent results in covariance matrix modelling, including the provision of unrestricted parametrizations of the space of correlation matrices, an alternative to a recent result utilizing the matrix logarithm.
