Accelerated sequential estimation of the mean

Accelerated sequential fixed width interval procedure for estimating the mean of an arbitrary distribution is considered. This procedure is an adaptation of Hall's procedure for fixed-width interval estimation of the mean of a normal population with unknown variance. First order asymptotics for the efficiency and the consistency of the sequential procedure are obtained. Second order asymptotic expansion for the expected stopping time is derived. The second order asymptotic results are illustrated by applying them to the sequential estimation of the mean of certain well-known distributions. Certain technical lemmas are given in the appendix.