On the estimation of the mean of a Np([mu],[Sigma]) population with [mu]'[Sigma]-1 [mu] known

We derive an explicit expression for the best equivariant estimator of a multivariate normal mean [mu] under the restriction [mu]'[Sigma]-1 [mu] = [lambda]0 as proposed by Kariya (1988). Its efficiency in comparison with linear and maximum likelihood estimation is also studied.