An optimal purely sequential strategy with asymptotic second-order properties: Applications from statistical inference and data analysis

Abstract

We develop a new class of purely sequential methodologies under an assumption that the population distribution belongs to a location-scale family. Both asymptotic first-order and second-order theories are put forward with substantial generality under a big and unified tent that successfully lead to a broad set of illustrations. After we identify an appropriately defined optimal strategy under this unified structure, we introduce applications that handle a variety of interesting inference problems. These are associated with, but not limited to, the following areas: (a) the fixed-width confidence interval (FWCI) estimation, (b) the minimum risk point estimation (MRPE), (c) the fixed-size confidence region (FSCR) estimation, (d) multiple comparisons, and (e) selecting the best normal treatment (StBNT). In illustrations (a)–(d), we have highlighted a number of choices of population distributions. Some illustrations are accompanied with data analyses.

KEYWORDS:

• Asymptotics
• exponential scale
• first-order properties
• fixed-size confidence region (FSCR)
• fixed-width confidence interval (FWCI)
• minimum risk point estimation (MRPE)
• multiple comparisons
• negative exponential location
• normal means
• optimal strategy
• scale family
• second-order properties
• selection and ranking

SUBJECT CLASSIFICATIONS:

• 62L10
• 62L05
• 62L12
• 62F25

ACKNOWLEDGMENTS

We are indebted to the handling Editor, Professor T. K. S. Solanky, an anonymous Associate Editor, and the two anonymous reviewers for their detailed critical and encouraging feedback on an earlier version of this work. Their thoughtful input has made a difference in preparing this revised version. We thank them all.

DISCLOSURE

The authors have no conflicts of interest to report.