Estimation of variance in an ANOVA setup

In an ANOVA setup one tests the global null hypothesis against the alternative
that at least one pair of means differ. In this paper we consider the estimation of
the variance, when it is suspected, but one is not sure, that the null hypothesis
holds. We consider the (i) unrestricted unbiased estimator (UUE), (ii) unrestricted
biased estimator (UBE), (iii) restricted unbiased estimator (RUE), (iv)
restricted biased estimator (RBE), (v) preliminary test estimator (PTE) using
UUE and RUE, (vi) Stein-type estimator (SE) using UBE and RBE of variance.
We derive the bias and risk expressions for these estimators to compare them. It
is shown that Stein-type estimator (SE) dominates uniformly over the UUE as
well as the PTE when the critical value for preliminary test is 1.