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

We consider the problem of estimating the scale parameter θθ 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 θθ, is proposed. A numerical study is performed and shows that the improved estimator yields significant risk reduction over the MRE.