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...

Near collinearities among explicative variables in a regression model have unwanted effects on the least squares estimator. They inflate the variances of least squares regression coefficient estimates and introduce a lack of fiability for this estimator. In this paper, we define precisely the...

A rule for choosing among nested models is presented, taking into account that the usual model selection procedure is a sequence of tests, followed by estimation of the parameters that remain in the model. We take a decision theoretical approach and formulate the loss functions and the rules...