Some remarks on estimating a noncentrality parameter

For the problem of estimating the concentrality parameter of a noncentral chi-square random variable X with a degrees of free-dom, it is shown that the Bayesian approach leads approximately to the same estimator X-a as the frequency approach, contrary to suggestions of de waal. Nonlinear estimators uniformly better than X-a are obtained by an empirical Bayes method. Similar results are obtained for the noncentral F distribution.