A note on estimating the common mean of k normal distributions and the stein problem

An unbiased estimator for the common mean of k normal distributions is suggested. A necessary and sufficient condition for the estimator Lo have a smaller variance than each sample mean is given. In the case of estimating the common mean vector of k p-variate (p ≤ 3) normal distributions a combined unbiased estimator may be used. We give a class of estimators which are better than the combined estimator when the loss is quadratic and the restriction of unbiasedness is removed.