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 α and β, respectively, we are interested in Thompson shrinkage test estimation for the shape parameter α under the Squared Log Error Loss (SLEL) function. We find a risk-unbiased estimator for α and compute its risk under the SLEL. According to Thompson (1986), we construct the pretest shrinkage (PTS) estimators for α with the help of a point guess value α₀ 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.