Inadmissibility of an estimator for the ratio of variance components

The problem of estimation of the ratio of variance components is considered from the invariance point of view. This approach actually paves the way for proving the inadmissibility of the optimal estimator developed by Loh (1986). A class of shrinkage estimators is also proposed. These estimators dominate the ML, REML and even in some cases, Bayes modal estimators, although this is not true for the optimal estimator. Numerical comparisons are made to establish the appealing behaviour of the proposed estimators.