An Investigation and Development of Three Estimators of Inverse Covariance Matrices with Applications to the Mahalanobis Distance

This paper treats the problem of estimating the inverse covariance matrix in an increasing dimension context. Specifically, three ridge-type estimators are considered, of which two new are proposed by the authors and one has been considered previously. Risk functions for deciding an appropriate value of the ridge coefficient are developed and the finite sample properties of the estimators are investigated in a Monte Carlo simulation. Moreover, risk functions for the Mahalanobis distance are derived which, in turn, leads to three new estimators which has not been considered previously