Improved estimation of an exponential scale ratio based on records

We consider the problem of estimating the ratio [theta] 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 [theta] 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.