On improved estimation of a gamma shape parameter

This paper deals with improved estimation of a gamma shape parameter from a decision-theoretic point of view. First we study the second-order properties of three estimators – (i) the maximum-likelihood estimator (MLE), (ii) a bias corrected version of the MLE, and (iii) an improved version (in terms of mean squared error) of the MLE. It is shown that all the three estimators mentioned above are second-order inadmissible. Next, we obtain superior estimators which are second order better than the above three estimators. Simulation results are provided to study the relative risk improvement of each improved estimator over the MLE.