James–Stein type estimators of variances

In this paper we propose James–Stein type estimators for variances raised to a fixed power by shrinking individual variance estimators towards the arithmetic mean. We derive and estimate the optimal choices of shrinkage parameters under both the squared and the Stein loss functions. Asymptotic properties are investigated under two schemes when either the number of degrees of freedom of each individual estimate or the number of individuals approaches to infinity. Simulation studies indicate that the performance of various shrinkage estimators depends on the loss function, and the proposed estimator outperforms existing methods under the squared loss function.