SEQUENTIAL POINT ESTIMATION OF THE POWERS OF AN EXPONENTIAL SCALE PARAMETER

摘要

In this paper we consider the bounded risk point estimation problem for the power of scale parameter σ~r of a negative exponential distribution where r ≠ 0 is any given number and the location parameter μ and scale parameter a both are unknown. For a preassigned error bound w > 0 we want to estimate σ~r by using a random sample of the smallest size such that the risk associated with an estimator is not greater than w. We propose a fully sequential procedure and give the asymptotic expansions of its average sample size and risk. We aso consider a class of sequential estimators based on the idea of bias-correction and make a comparison from the point of view of risk.