Suppose that one can observe bivariate random variables (L,X) only when L≤X holds. Such data are called left-truncated data and found in many fields, such as experimental education and epidemiology. Recently, a method of fitting a parametric model on (L,X) has been considered, which can easily...

Many statistical methods for truncated data rely on the independence assumption regarding the truncation variable. In many application studies, however, the dependence between a variable X of interest and its truncation variable L plays a fundamental role in modeling data structure. For...

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...