Lattice conditional independence (LCI) models introduced by S. A. Andersson and M. D. Perlman (1993, Ann. Statist.21, 1318-1358) have the pleasant feature of admitting explicit maximum likelihood estimators and likelihood ratio test statistics. This is because the likelihood function and...

The problem of estimating large covariance matrices of multivariate real normal and complex normal distributions is considered when the dimension of the variables is larger than the number of samples. The Stein-Haff identities and calculus on eigenstructure for singular Wishart matrices are...

The problem of estimating the precision matrix of a multivariate normal distribution model is considered with respect to a quadratic loss function. A number of covariance estimators originally intended for a variety of loss functions are adapted so as to obtain alternative estimators of the...

Let X be an m - p matrix normally distributed with matrix of means B and covariance matrix Im [circle times operator] [Sigma], where [Sigma] is a p - p unknown positive definite matrix. This paper studies the estimation of B relative to the invariant loss function tr . New classes of invariant...

In this paper the problem of estimating a covariance matrix parametrized by an irreducible symmetric cone in a decision-theoretic set-up is considered. By making use of some results developed in a theory of finite-dimensional Euclidean simple Jordan algebras, Bartlett's decomposition and an...

We consider stochastic domination in predictive density estimation problems when the underlying loss metric is α-divergence, D(α), loss introduced by Csiszàr (1967). The underlying distributions considered are normal location-scale models, including the distribution of the observables, the...

This paper is concerned with estimation of a predictive density with parametric constraints under Kullback–Leibler loss. When an invariance structure is embedded in the problem, general and unified conditions for the minimaxity of the best equivariant predictive density estimator are derived....

We investigate conditions under which estimators of the form X + aU'Ug(X) dominate X when X, a p - 1 vector, and U, an m - 1 vector, are distributed such that [X1, X2,..., Xp, U1, U2,..., Up]'/[sigma] has a spherically symmetric distribution about [[theta]1, [theta]2,..., [theta]p, 0, 0,...,...

We consider the problem of estimating a p-dimensional parameter [theta]=([theta]1,...,[theta]p) when the observation is a p+k vector (X,U) where dim X=p and where U is a residual vector with dim U=k. The distributional assumption is that (X,U) has a spherically symmetric distribution around...

Assume X = (X1, ..., Xp)' is a normal mixture distribution with density w.r.t. Lebesgue measure, , where [Sigma] is a known positive definite matrix and F is any known c.d.f. on (0, [infinity]). Estimation of the mean vector under an arbitrary known quadratic loss function Q([theta], a) = (a -...