ON RANK ESTIMATION IN SYMMETRIC MATRICES: THE CASE OF INDEFINITE MATRIX ESTIMATORS

In this paper we consider estimating the rank of an unknown symmetric matrix based on a symmetric, asymptotically normal estimator of the matrix+ The related positive definite limit covariance matrix is assumed to be estimated consistently and to have either a Kronecker product or an arbitrary structure+ These assumptions are standard although they exclude the case when the matrix estimator is positive or negative semidefinite+ We adapt and reexamine here some available rank tests and introduce a new rank test based on the sum of eigenvalues of the matrix estimator+ We discuss two applications where rank estimation in symmetric matrices is of interest, and we also provide a small simulation study+