Statistical proofs of some matrix inequalities Original Research Article

Matrix algebra is extensively used in the study of linear models and multivariate analysis (see for instance Refs. [18,21]). During recent years, there have been a number of papers where statistical results are used to prove some matrix theorems, especially matrix inequalities (Refs. [5,7,8,10,14,15]). In this paper, a number of matrix results are proved using some properties of Fisher information and covariance matrices. A unified approach is provided through the use of Schur complements. It may be noted that the statistical results used are derivable without using matrix theory.