# Double stage estimation of population variance

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## Summary

Consider a normal population with mean μ and variance σ^{2}. We are interested in the estimation of population variance with the help of guess value σ _{0} ^{2} and a sample of observations. In this paper, a double stage shrinkage estimator\(\hat \sigma _k^2 \) based on the shrinkage estimator*ks* _{1} ^{2} +(1-*k*)σ _{0} ^{2} if*s* _{1} ^{2} ∈*R* and the usual estimator\(s^2 = \frac{{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2 }}{{n_1 + n_2 - 2}}\) if*s* _{1} ^{2} ∋*R*, where*R* is some specified region, have been proposed. The expressions for bias and mean squared error have been obtained. Comparison with the usual estimator*s*^{2} have been made. It was found that though the largest gain is obtained for*k*=0, we can use\(\hat \sigma _k^2 \) with 0≦*k*≦1/2 even when σ^{2} is very close to σ _{0} ^{2}

## Keywords

Shrinkage Normal Population Population Variance Usual Estimator Large Gain## Preview

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## References

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