A note on the equivariant estimation of an exponential scale using progressively censored data

We consider the problem of estimating the scale parameter θ of the shifted exponential distribution with unknown location based on a type II progressively censored sample. Under a large class of bowl-shaped loss functions, a smooth estimator, that dominates the minimum risk equivariant estimator of θ , is proposed. A numerical study is performed and shows that the improved estimator yields significant risk reduction over the MRE.