Purely sequential estimation problems for the mean of a normal population by sampling in groups under permutations within each group and illustrations

Abstract

Abstract Purely sequential estimation for unknown mean ( ) in a normal population having an unknown variance ( ) when observations are gathered in groups has been recently discussed in Mukhopadhyay and Wang (2020). In this article, we briefly revisit two fundamental problems on sequential estimation: (i) the fixed-width confidence interval (FWCI) estimation problem and (ii) the minimum risk point estimation (MRPE) problem. However, we substitute the estimators defining the stopping boundaries with newly constructed unbiased and consistent estimators under permutations within each group. These new estimators incorporated in the definition of the stopping boundaries have led to tighter estimation of requisite optimal fixed sample sizes. We have analyzed the first-order and second-order asymptotic properties under appropriate requirements on the pilot size. Large-scale computer simulations and substantial data analysis have validated such first-order and second-order results. The methodologies are illustrated with the help of time series data on offshore wind energy.