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 $0<\rho <1$ 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 ${\rho }^{-1}$ was not an integer. First time in the literature, we have recently designed acceleration with asymptotic s.o. expansions in normal mean problems with ${\rho }^{-1}$ arbitrary. In this article, a general unified theory is now developed leading to asymptotic s.o. expansions for customarily studied characteristics with arbitrary ${\rho }^{-1}.$ 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.

Keywords:

• Distribution-free
• exponential distribution
• general theory
• negative exponential
• nonlinear renewal theory
• one-sample
• second-order expansions
• two-sample

SUBJECT CLASSIFICATIONS:

• 62L05
• 62L10
• 62L12
• 62L99

ACKNOWLEDGMENTS

We express our deep gratitude to the handling Editor-in-Chief, Professor Tumulesh K. S. Solanky; an anonymous associate editor; and the two anonymous reviewers. The critical assessments and thoughtful comments received from them helped us tremendously to come up with this improved version. We sincerely thank them all.

DISCLOSURE

The authors have no conflicts of interest to report.