Pretest shrinkage estimators for the shape parameter of a Pareto model using prior point knowledge and record observations

Abstract

Considering a Pareto model with unknown shape and scale parameters \(\alpha\) and \(\beta\), respectively, we are interested in Thompson shrinkage test estimation for the shape parameter \(\alpha\) under the Squared Log Error Loss (SLEL) function. We find a risk-unbiased estimator for \(\alpha\) and compute its risk under the SLEL. According to Thompson (1986), we construct the pretest shrinkage (PTS) estimators for \(\alpha\) with the help of a point guess value \(\alpha_0\) and record observations. We investigate the risk-bias of these estimators and compute their risks numerically. A comparison is performed between the PTS estimators and a risk-unbiased estimator. A numerical example is presented for illustrative and comparative purposes. We end the paper by discussion and concluding remarks.