Sequential Estimation of a Common Location Parameter of two Populations

Abstract

The problem of sequentially estimating a common location parameter of two independent populations from the same distribution with an unknown location parameter and known but different scale parameters is considered in the case when the observations become available at random times. Certain classes of sequential estimation procedures are derived under a location invariant loss function and with the observation cost determined by convex functions of the stopping time and the number of observations up to that time.