On the estimation of a normal precision and a normal variance ratio

The problem of estimating the ratio of the variances of two independent normal populations is considered under both quadratic and entropy losses, when the means are unknown. New classes of improved estimators are obtained with the following properties. They are smooth, improve on the risk of the best affine equivariant estimator at every parameter point, have very simple form and are based on all the available data. In the case of entropy loss, the estimators of one of these classes are, additionally, generalized Bayes. Our approach for constructing these improved estimators is based on Strawderman’s (1974) [18] technique. As a preliminary result of independent interest, new classes of dominating generalized Bayes procedures for a normal precision are also given.