Abstract. In the present paper, we study shrinkage testimation for the unknown scale parameter θ > 0 of the exponential distribution based on record data under the asymmetric squared log error loss function. A minimum risk unbiased estimator within the class of the estimators of the form cT m is derived, where T m is the maximum likelihood estimate of θ. Some shrinkage testimators are proposed and their risks are computed. The relative efficiencies of the shrinkage testimators with respect to a minimum risk unbiased estimator of the form cT m under the squared log error loss function are calculated for the comparison purposes. An illustrative example is also presented.

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.