Abstract

Purely sequential decision strategies to develop a fixed-width confidence interval (FWCI) or a
minimum risk point estimator (MRPE) for the mean of a normal (or another) distribution with an unknown variance are well-known in the literature. I will begin there. Under purely sequential decision strategies, one frequently comes up with asymptotic second-order (s.o.) expansions of many requisite characteristics.

In a parallel development, accelerated sequential decision strategies are known to be logistically more convenient to apply than purely sequential counterparts, and there exists a rich literature on 100a% acceleration (0 < a < 1) to obtain either FWCI or MRPE for the unknown mean b in a Normal (b,c) distribution with an unknown variance c. Under acceleration, however, one frequently comes up with asymptotic s.o. lower/upper bounds for many requisite characteristics when 0 < a < 1 is arbitrary but 1/a is not an integer.

We revisit the most improved and well-known acceleration technique under arbitrarily fixed 0 < a < 1 and modify it suitably to develop asymptotic s.o. expansions for the first time in the literature (instead of s.o. lower/upper bounds) in the said FWCI and MRPE problems. We will emphasize the new methodology behind this long overdue success followed by analysis of data from simulations.