Title: Covariance structure induced by sparsity in non-standard domains
Authors: Heather Battey - Imperial College London and Princeton University (United Kingdom) [presenting]
Abstract: An estimate of a covariance or inverse covariance matrix is an essential ingredient in many multivariate statistical procedures. When the dimension of the matrix is large relative to the sample size, the sample covariance matrix is inconsistent in the matrix norms relevant for applications and its non-invertibilty renders many techniques in multivariate analysis infeasible. Structural assumptions are necessary in order to restrain the estimation error, even if this comes at the expense of some approximation error if the structural assumptions fail to hold. We will discuss the non-sparse structure induced on the original space of covariance matrices by imposing sparsity in the matrix logarithmic domain. We will also show the converse result that any covariance matrix possessing such structure is logarithmically sparse. Generalisations of this structure will then be discussed.