TRANSFORMATION OF NONPOSITIVE SEMIDEFINITE CORRELATION-MATRICES

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 axe 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.