On the maximum-entropy approach to undersized samples

Abstract

In the context of estimating a covariance matrix, the problem of undersized samples occurs when the number of sample observations is less than the number of variables. One possible solution to such problems as they arise in the estimation of covariance matrices, and more general multivariate analyses, is provided by the maximum-entropy (ME) distribution and its covariance matrix. This paper addresses two questions that are often posed with regard to the ME covariance matrix: (1) Does the procedure involve a heavy computational burden? (2) How does it relate to the solutions provided by generalized inverses?