Decision theoretic estimation using record statistics

We consider the problem of estimating the scale parameter θ of the shifted exponential distribution with unknown shift based on a set of observed records drawn from a sequential sample of independent and identically distributed random variables. Under a large class of bowl-shaped loss functions, the best affine equivariant estimator (BAEE) of θ is shown to be inadmissible. Two dominating procedures are proposed. A numerical study is performed to show the extent of risk reduction that the improved estimators provide over the BAEE.