Preference for a class of super-efficient estimators of the normal mean: A study on sample size requirement

Abstract

A class of super-efficient estimators of the mean of a normal population with unit variance has been recently constructed by Sivasakthi et al. (2016) through the ‘Delta Method’. Theoretically, a super-efficient estimator is preferable to the asymptotically efficient estimator (could be the maximum likelihood estimator) in a large-sample context. In this paper, we address the super-efficient estimation of the normal mean when the population variance is known. The important question on the sample size required for a super-efficient estimator to be preferred over the (asymptotically) efficient estimator / maximum likelihood estimator is addressed through a numerical study. The answer to the question is sought for a chosen subset of the class of super-efficient estimators under consideration.