Transformation of Non Positive Semidefinite Correlation Matrices

Abstract

In multivariate statistics, estimation of the covariance or correlation matrix is of crucial importance. Computational and other arguments often lead to the use of coordinate-dependent estimators, yielding matrices that are symmetric but not positive semidefinite. We briefly discuss existing methods, based on shrinking, for transforming such matrices into positive semidefinite matrices. A simple method based on eigenvalues is also considered. Taking into account the geometric structure of correlation matrices, a new method is proposed which uses techniques similar to those of multidimensional scaling.