ESTIMATION OF GENERALIZED VARIANCE, PRECISION AND COVARIANCE MATRICES USING THE PITMAN NEARNESS CRITERION

The problem of preferring one estimator of SIGMA over another is considered within the class of estimators a(i)S, i = 1, 2, where S approximately W(p)(n - 1, SIGMA). Computer simulations are performed to demonstrate the conditions on the a(i), i = 1, 2 under the loss function L(SIGMA, SIGMA) = tr SIGMASIGMA-1 + tr SIGMA-1SIGMA - 2p. The asymptotic probability of closeness of such estimators is obtained. Estimation of the precision matrix and the generalized variance is also considered using the Pitman nearness criterion. Finally an estimator of the signal to noise ratio is studied.