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On Double Stage Shrinkage Estimator For the Variance of Normal Distribution With Unknown Mean

Author: Muna D. Salman
Journal: Ibn Al-Haitham Journal For Pure And Applied Science مجلة ابن الهيثم للعلوم الصرفة والتطبيقية ISSN: P16094042/ E25213407 Year: 2017 Volume: 30 Issue: 2 Pages: 177-191
Publisher: Baghdad University جامعة بغداد

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Abstract

This paper is concerned with preliminary test double stage shrinkage estimators toestimate the variance (2) of normal distribution when a prior estimate 20 ( ) of the actualvalue (2) is a available when the mean is unknown , using specifying shrinkage weightfactors () in addition to pre-test region (R).Expressions for the Bias, Mean squared error [MSE ()], Relative Efficiency [R.EFF ()],Expected sample size [E(n/2)] and percentage of overall sample saved of proposed estimatorwere derived. Numerical results (using MathCAD program) and conclusions are drawn aboutselection of different constants including in the mentioned expressions. Comparisons betweenthe suggested estimator with the classical estimator in the sense of Bias and RelativeEfficiency are given. Furthermore, comparisons with the earlier existing works are drawn.

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