ABSTRACT
It is well known that if the dimension p of the normal random vector is unity, the sample mean is minimax and admissible for the population mean with the squared error loss function (see for example Giri (1993)). As we have seen earlier for general p the sample mean is minimax for the population mean with the quadratic error loss function. However, Stein (1956) has shown that the square error loss function and S=I (identity matrix), is admissible for p=2 and it becomes inadmissible for p=3. He showed that estimators of the form
dominates for a sufficiently small a and b sufficiently large for p=3. James and Stein (1961) improved this result and showed that even with one observation on the random vector X having p-variate normal distribution with mean µ and covariance matrix S=I the class of estimators
dominates X for p=3. Their results led many researchers to work in this area which produced an enormous amount of rich literature of considerable importance in statistical theory and practice. Actually this estimator is a special
