(Received March 8, 1993; revised September 20, 1993)
Abstract. Both one-sample and multi-sample estimation problems for the means of one parameter exponential distributions are addressed. In the one-sample case, for the existing purely sequential and recently obtained piecewise sequential estimation methodologies, we follow and extend the development in Isogai and Uno (1993, Ann. Inst. Statist. Math. (in press)) in order to obtain a class of estimators that provides asymptotic second-order risk improvement. In the multi-sample problem, we address the analogous aspects for the existing purely sequential methodology as well as the newly developed piecewise methodology.
Key words and phrases: Risk improvement, second-order asymptotics, exponential distributions, sequential methods, piecewise sequential methods, one-sample problems, multi-sample problems.