Minimax Estimation of a Normal Mean Vector When the Covariance Matrix is Unknown

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...

Minimax Estimation of a Mean Vector

K E Y W O R D S AND PHRASES Minimax decision rule; squared error loss; Dirichlet process; compact sets; Bayes rules; isotonic regression. l . INTRODUCTION In an often cited paper, BOHLMANN (1976) has considered linear minimax estimators for the mean of a univariate distribution in a nonparametr ic setting under squared error loss. To be precise, BOHLMANN assumes that Fo(x ) is a family of C D F...

Estimation of Covariance Matrix in Signal Processing When the Noise Covariance Matrix is Arbitrary

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...

Accurate critical constants for the one-sided approximate likelihood ratio test of a normal mean vector when the covariance matrix is estimated.

Tang, Gnecco, and Geller (1989, Biometrika 76, 577-583) proposed an approximate likelihood ratio (ALR) test of the null hypothesis that a normal mean vector equals a null vector against the alternative that all of its components are nonnegative with at least one strictly positive. This test is useful for comparing a treatment group with a control group on multiple endpoints, and the data from t...