Shrinkage Testimation in Exponential Distribution based on Records under Asymmetric Squared Log Error Loss

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 cTm is derived, where Tm 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 cTm under the squared log error loss function are calculated for the comparison purposes. An illustrative example is also presented.