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Abstract
Research on classical fixed-width confidence interval (FWCI) estimation problems for a normal mean when the variance remains unknown have steadily moved along under a zero-one loss function. On the other hand, minimum risk point estimation (MRPE) problems have grown largely under a squared error loss function plus sampling cost. However, the FWCI problems customarily do not take into account any sampling cost in their formulations. This fundamental difference between the two treatments has led the literature on the FWCI and MRPE problems to grow in multiple directions in their own separate ways from one another. In this article, we introduce a new formulation combining both MRPE and FWCI methodologies with desired asymptotic first-order (Theorems 2.1–2.2) and asymptotic second-order characteristics (Theorem 2.3) under a single unified structure, allowing us to develop a genuine minimum risk fixed-width confidence interval (MRFWCI) estimation strategy. Fruitful ideas are proposed by incorporating illustrations from purely sequential and other multistage MRFWCI problems with an explicit presence of a cost function incurred due to sampling. We supplement the general theory and methodology by means of illustrations and analyses from simulated data along with applications to air quality data.
ACKNOWLEDGMENTS
We are indebted to the handling Editor, Professor T. K. S. Solanky, the anonymous Associate Editor, and two reviewers for their detailed critic of an earlier version of this work. Their thoughtful input has made a big difference in preparing this improved revised version. We thank them all.
DISCLOSURE
The authors have no conflicts of interest to report.