Banded approximation to inverses of bandedly approximable matrices 
       and operators with applications to covariance matrix estimation and 
       strong mixing of Gaussian processes 

                     Peter J. Bickel
            University of California, Berkeley 


Abstract: It is a well known result, based on the theory of C* algebras, that 
the operator norm closure of banded operators from l_2 to l_2 is closed under 
inversion. We make this result explicit by giving bounds on operator norm 
approximation by banded matrices to the inverse of a matrix M given a bound on 
the approximation by banded matrices to M. These results and generalizations are 
used to derive properties of methods of estimation of sparse (in a suitable sense) 
high dimensional covariance matrices and their inverses and to derive a simple 
strong mixing condition for general (nonstationary) Gaussian processes.

(joint work with M. Lindner (Chemnitz))