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.