Estimating Fisher information in normal population with prior information

Abstract

This paper is contemplated to propose a class of shrunken estimators which is further used in constructing a class of preliminary test estimators for amount of information in complete samples from normal population when some ‘apriori’ or guessed value of amount of information is available and analyses their characteristics. The proposed classes of shrunken estimators and preliminary test estimators are compared with the usual unbiased estimator and MMSE estimator. Eventually, empirical study is carried out to demonstrate the performance of some shrunken estimators and preliminary test estimators of the proposed classes over the MMSE estimator. The suggested class of estimators is found to give gratifying results. Subsequently, the usage of proposed classes of estimators in estimating the precision of sample mean has been exclusively discussed followed by an example.