On Double Stage Shrinkage Estimator For the Variance of Normal Distribution With Unknown Mean
Keywords:
Normal Distribution, Double Stage Shrinkage Estimator, Bias Ratio, Mean Squared Error , Relative Efficiency , Expected sample size. Percentage of overall sample saved and probability of avoiding the second sample .Abstract
This paper is concerned with preliminary test double stage shrinkage estimators to estimate the variance (s2) of normal distribution when a prior estimate of the actual value (s2) is a available when the mean is unknown , using specifying shrinkage weight factors y(×) in addition to pre-test region (R).
Expressions for the Bias, Mean squared error [MSE (×)], Relative Efficiency [R.EFF (×)], Expected sample size [E(n/s2)] and percentage of overall sample saved of proposed estimator were derived. Numerical results (using MathCAD program) and conclusions are drawn about selection of different constants including in the mentioned expressions. Comparisons between the suggested estimator with the classical estimator in the sense of Bias and Relative Efficiency are given. Furthermore, comparisons with the earlier existing works are drawn.
