Sequential Estimation Procedures for End Points of Support in a Non-Regular Distribution

Abstract

In this article, we consider sequential estimation of the end points of the support based on the extreme values when the underlying distribution has a bound support. Some sequential fixed-width confidence intervals are proposed. Stopping rules based on the range are proposed and the estimation procedures based on them are shown to be asymptotically efficient. The results of numerical simulations are presented. Moreover, the sequential point estimation problem is considered under squared loss plus cost of sampling.

Keywords:

• Asymptotic efficiency
• Sequential estimation
• Stopping rule

Mathematics Subject Classification:

• 62L12
• 62F25

Acknowledgments

I thank two anonymous referees for their valuable comments. I express my deep thanks to Dr. Shono of National Research Institute of Far Seas Fisheries of Japan, who gave advice on the references of fishery statistics. This research was partly supported by the Grant-in-Aid for Scientific Research (C) 17540101, Japan Society for the Promotion of Science.