Improved estimation of an exponential scale ratio based on records

We consider the problem of estimating the ratio θθ of the scale parameters of two shifted exponential distributions with unknown shifts, based on two independent samples of records drawn from sequential samples of independent and identically distributed random variables. Under a large class of bowl-shaped loss functions, the best affine equivariant estimator (BAEE) of θθ is shown to be inadmissible. Four new classes of dominating procedures are proposed. A numerical study is performed to show the extent of risk reduction that the improved estimators provide over the BAEE.