Pitman closeness of the class of isotonic estimators for ordered scale parameters of two Gamma distributions

The problem of estimating order-restricted scale parameters of two Gamma distributions is considered under the Pitman closeness criterion. A class of isotonic estimators including the MLE is proposed. Some properties of this class of isotonic estimators is given under the Pitman closeness criterion. In particular, some properties of the MLE naturally follow. We use simulation comparisons to examine the results. Copyright Springer-Verlag Berlin Heidelberg 2014