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...

The conditional autoregressive (CAR) and simultaneous autoregressive (SAR) models both have been used extensively for the analysis of spatial structure underlying lattice data in many areas, such as epidemiology, demographics, economics, and geography. Default Bayesian analyses have been...

We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, where the dimension p may be large. Gaussian graphical models provide an important tool in describing conditional independence through presence or absence of edges in the underlying graph. A...

This paper considers testing the equality of multiple high-dimensional mean vectors under dependency. We propose a test that is based on a linear transformation of the data by the precision matrix which incorporates the dependence structure of the variables. The limiting null distribution of the...

In this paper we propose James–Stein type estimators for variances raised to a fixed power by shrinking individual variance estimators towards the arithmetic mean. We derive and estimate the optimal choices of shrinkage parameters under both the squared and the Stein loss functions. Asymptotic...

Given a multinomial decomposable graphical model, we identify several alternative parametrizations; in particular we consider conditional probabilities of clique-residuals given separators, as well as generalized log-odds-ratios. For each such parametrization, we construct the corresponding...

Asymptotic cumulants of the Bayes and pseudo Bayes estimators of ability in item response theory are obtained up to the fourth order with the higher-order asymptotic variance under possible model misspecification. Typical estimators are treated as special cases of the (pseudo) Bayes estimator...

Differential entropy and log determinant of the covariance matrix of a multivariate Gaussian distribution have many applications in coding, communications, signal processing and statistical inference. In this paper we consider in the high-dimensional setting optimal estimation of the...

It turns out that there exist general covariance matrices associated not only to a random vector itself but also to its general moments. In this paper we introduce and characterize general covariance matrices of a random vector that are associated to some important general moments, which are...

This paper deals with the problem of estimating the normal covariance matrix relative to the Stein loss. The main interest concerns a new class of estimators which are invariant under a commutator subgroup of lower triangular matrices. The minimaxity of a James–Stein type invariant estimator...