The problem of the estimation of a multivariate normal mean when the variance is known up to a multiplicative factor is considered under an arbitrary quadratic loss. We introduce shrinkage estimators with differentiable shrinking functions under weak algebraic assumptions. We deduce sufficient...

When several simple regression models are assumed to have similar slopes, empirical Bayes methods can efficiently process tis vague information by estimating the hyperparameters of a conjugate prior. The shrinkage estimators we obtain are shown to be minimax and, furthermore, dominate usual...

The usual confidence set for a multivariate mean vector can be improved upon by recentering the set at a Stein-type estimator: this fact is known to be true under many different distributional assumptions. Thus far, however, the case of unknown variance has not been dealt with analytically. In...

Modified Bessel functions are often of use in the probabilistic and statistical analysis of spherical distributions and we give here the main properties of these functions. In particular, they appear in Bayes estimators with respect to uniform distributions on spheres; we derive a constructive...

In this paper, we study the basic properties of the generalized inverse normal distribution, natural alternative to the inverse Gaussian distribution, and we show that it generates a conjugate prior family in a normal estimation problem.