Theory and practice of second-order expansions for moments of 100ρ% accelerated sequential stopping times in parametric and nonparametric estimation with arbitrary fractional ρ

Abstract

Sampling strategies with fractional acceleration 0 < ρ < 1 achieve substantial operational savings compared with purely sequential counterparts. But, acceleration customarily yielded second-order (s.o.) lower and upper bounds for requisite characteristics when ρ − 1 was not an integer. First time in the literature, we have recently designed acceleration with asymptotic s.o. expansions in normal mean problems with ρ − 1 arbitrary. In this article, a general unified theory is now developed leading to asymptotic s.o. expansions for customarily studied characteristics with arbitrary ρ − 1 . That is, the previously known s.o. lower/upper bounds can be replaced with appropriate s.o. expansions in a variety of inference problems with prescribed accuracy. We emphasize the theoretical foundation and ensuing analyses with a series of interesting inference problems from (a) a number of non-normal distributions as well as (b) one- and two-sample distribution-free scenarios. These prove a desirable breadth of coverage under our proposed big tent.