Comparison of some sequential procedures with related optimal stopping rules

Summary For the problem of estimating the mean of independent, identically distributed random variables, with loss equal to a linear combination of squared error and sample size, certain sequential procedures have been shown to be asymptotically optimal when compared with the best fixed sample size rule. In this paper it is shown that these procedures are asymptotically suboptimal when compared with a closely related optimal stopping rule.A preliminary version of this paper was presented at the International Meeting on Sample Survey Analysis and on Sequential Analysis, Jerusalem, Israel, June 1982