Estimation of the Shape Parameter of the Gamma Distribution

The problem of estimation of an unknown shape parameter under the sample drawn from the gamma distribution, where the scale parameter is also unknown, is considered. A new estimator, called the maximum likelihood scale invariant estimator, is proposed. It is established that the mean square error of this estimator is less than that of the usual maximum likelihood estimator. The asymptotics of the mean square error of the new estimator is also obtained