Fixed precision estimation of a normal mean

Estimation of the Multivariate Normal Mean under the Extended Reflected Normal Loss Function

Discriminative estimation of subspace precision and mean (SPAM) models

The SPAM model was recently proposed as a very general method for modeling Gaussians with constrained means and covariances. It has been shown to yield significant error rate improvements over other methods of constraining covariances such as diagonal, semi-tied covariances, and extended maximum likelihood linear transformations. In this paper we address the problem of discriminative estimation...

On minimax estimation of a sparse normal mean vector

Mallows has conjectured that among distributions which are Gaussian but for occasional contamination by additive noise, the one having least Fisher information has (two-sided) geometric contamination. A very similar problem arises in estimation of a non-negative vector parameter in Gaussian white noise when it is known also that most, i.e. (1 − ǫ), components are zero. We provide a partial asym...

Improved minimax estimation of a multivariate normal mean under heteroscedasticity

Consider the problem of estimating a multivariate normal mean with a known variance matrix, which is not necessarily proportional to the identity matrix. The coordinates are shrunk directly in proportion to their variances in Efron and Morris’ (J. Amer. Statist. Assoc. 68 (1973) 117–130) empirical Bayes approach, whereas inversely in proportion to their variances in Berger’s (Ann. Statist. 4 (1...

A Note on the Bounded Normal Mean Estimation

The bounded normal mean problem has important applications in nonparametric function estimation. It is to estimate the mean of a normal distribution whose mean is restricted to a bounded interval. The minimax risk for such a problem is generally unknown. It is shown in Donoho, Liu and MacGibbon(1990) that the linear minimax risk provides a good approximation to the minimax risk. We show in this...