Sequential Determination of Estimator as Well as Sample Size

Abstract

For certain point and interval estimation problems, sequential procedures are proposed for choosing an estimator (from the class of trimmed means with trimming proportion in a specified range) as well as a sample size on which to base the estimator. It is shown that these procedures, which do not require knowledge of the best trimming proportion or the asymptotic variance of the corresponding trimmed mean, are asymptotically efficient with respect to the procedure that uses the best trimmed mean (in the specified class) and the best fixed sample size for that trimmed mean.