We investigate the problem of estimating the Cholesky decomposition in a conditional independent normal model with missing data. Explicit expressions for the maximum likelihood estimators and unbiased estimators are derived. By introducing a special group, we obtain the best equivariant estimators.

It is well known that the best equivariant estimator of the variance covariance matrix of the multivariate normal distribution with respect to the full affine group of transformation is not even minimax. Some minimax estimators have been proposed. Here we treat this problem in the framework of a...

With sparse structures and conditional independence, one could estimate the precision matrix of Gaussian graphical models more efficiently. Sun and Sun (2005) studied objective priors for star-shape graphical models. We consider a generative star-shape model. Objective priors such as invariance...

Objective Bayesian inference procedures are derived for the parameters of the multivariate random effects model generalized to elliptically contoured distributions. The posterior for the overall mean vector and the between-study covariance matrix is deduced by assigning two noninformative priors...

The issue of objective prior specification for the parameters in the normal compositional model is considered within the context of statistical analysis of linearly mixed structures in image processing. In particular, the Jeffreys prior for the vector of fractional abundances in case of a known...