Some classes of shrinkage estimators for estimating the standard deviation towards an interval of normal distribution

Abstract

The present paper investigates some classes of shrinkage estimators for estimating standard deviation in the case of univariate normal parent when some a priori or guessed interval containing this parameter is available from past experience. The need to study this parameter arises owing to its importance in estimating different parametric functions such as mean deviation about mean, standard deviation, standard error of mean and coefficient of variation with known mean. Numerical illustrations are given in support to the present study. Simulation studies confirm the high efficiency of the developed classes of shrinkage estimators when compared with their usual unbiased estimator and minimum mean squared error (MMSE) estimators.