Sequential interval estimation via replicated piecewise stopping times and accelerated stopping times in a class of two-parameter exponential family of distributions

Abstract

We reconsider the problem of constructing interval estimate of fixed proportional accuracy as introduced in Bose and Boukai (1993b). We discuss two approaches to make their fully sequential procedure operationally more attractive. First, we propose to implement their sequential procedure in smaller pieces along the lines of Mukhopadhyay and Sen (1993). Second, we perform purely sequential sampling part of the way, followed by appropriate batch sampling. In either case we provide the second-order expansion of the coverage probability and these compare well with that of the full sequential procedure. Along the way we also relax some of the technical restrictions of Bose and Boukai (1993b).