EDA on the asymptotic normality of the standardized sequential stopping times, Part-II: Distribution-free models

Abstract

In sequential analysis, an experimenter gathers information regarding an unknown functional (parameter) by observing random samples in successive steps. We discuss a number of distribution-free scenarios under a variety of loss functions. The number of observations gathered upon termination is a positive integer-valued random variable, customarily denoted by N. Often, a standardized version of N would follow an approximate normal distribution in the asymptotic sense. We provide exploratory data analysis (EDA) with the help of a number of interesting illustrations. We do so via large-scale simulation studies to demonstrate broad applicability of the purely sequential methodologies along with the appropriateness of asymptotic normality of the standardized stopping variables as a practical and useful guideline.

Keywords:

• Asymptotics
• exploratory data analysis
• fixed-width confidence interval
• mean estimation
• minimum risk point estimation
• nonparametrics
• squared error loss
• standardized stopping time
• unknown distribution
• variance estimation

SUBJECT CLASSIFICATIONS:

• 62L12
• 62L10
• 62E17

ACKNOWLEDGMENTS

Chen Zhang carried out this research at the University of Connecticut–Storrs as a part of his PhD dissertation. An associate editor and a referee gave valuable comments on an earlier version. This presentation benefited from their enthusiastic feedback. We thank both the Associate Editor and the referee for their kind help.

DISCLOSURE

The authors have no conflicts of interest to report.