GENERAL CLASSES OF SHRINKAGE ESTIMATORS FOR THE MULTIVARIATE NORMAL MEAN WITH UNKNOWN VARIANCE: MINIMAXITY AND LIMIT OF RISKS RATIOS

In this paper, we consider two forms of shrinkage estimators of the mean theta of a multivariate normal distribution X similar to N-p (theta, sigma(2) I-p) in IkP where sigma(2) is unknown and estimated by the statistic S-2 (S-2 similar to sigma(2)chi(2)(n)). Estimators that shrink the components of the usual estimator X to zero and estimators of Lindley-type, that shrink the components of the usual estimator to the random variable (X) over bar. Our aim is to improve under appropriate condition the results related to risks ratios of shrinkage estimators, when n and p tend to infinity and to ameliorate the results of minimaxity obtained previously of estimators cited above, when the dimension p is finite. Some numerical results are also provided.