Double stage estimation of population variance

Summary

Consider a normal population with mean μ and variance σ². We are interested in the estimation of population variance with the help of guess value σ ²₀ and a sample of observations. In this paper, a double stage shrinkage estimator$\hat \sigma _k^2$ based on the shrinkage estimatorks ²₁ +(1-k)σ ²₀ ifs ²₁ ∈R and the usual estimator$s^2 = \frac{{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2 }}{{n_1 + n_2 - 2}}$ ifs ²₁ ∋R, whereR is some specified region, have been proposed. The expressions for bias and mean squared error have been obtained. Comparison with the usual estimators ² have been made. It was found that though the largest gain is obtained fork=0, we can use$\hat \sigma _k^2$ with 0≦k≦1/2 even when σ² is very close to σ ²₀