On rank estimation in semidefinite matrices

This work concerns the problem of rank estimation in semidefinite matrices, having either indefinite or semidefinite matrix estimator satisfying a typical asymptotic normality condition. Several rank tests are examined, based on either available rank tests or basic new results. A number of related issues are discussed such as the choice of matrix estimators and rank tests based on finer assumptions than those of asymptotic normality of matrix estimators. Several examples where rank estimation in semidefinite matrices is of interest are studied and serve as guide throughout the work.