Three-Stage Sequential Estimation of the Inverse Coefficient of Variation of the Normal Distribution

Abstract

This paper sequentially estimates the inverse coefficient of variation of the normal distribution using Hall’s three-stage procedure. We find theorems that facilitate finding a confidence interval for the inverse coefficient of variation that has pre-determined width and coverage probability. We also discuss the sensitivity of the constructed confidence interval to detect a possible shift in the inverse coefficient of variation. Finally, we find the asymptotic regret encountered in point estimation of the inverse coefficient of variation under the squared-error loss function with linear sampling cost. The asymptotic regret provides negative values, which indicate that the three-stage sampling does better than the optimal fixed sample size had the population inverse coefficient of variation been known.