In this paper, we consider estimating the Cholesky decomposition (the lower triangular squared root) of the covariance matrix for a conditional independent normal model under four equivariant loss functions. Closed-form expressions of the maximum likelihood estimator and an unbiased estimator of...

In a heteroskedastic partially linear regression model, You and Chen (Technical Report, Department of Mathematics and Statistics, University of Regina, 2000) proposed a semiparametric generalized least squares estimator (SGLSE). In this paper, a jackknife-type estimator of the asymptotic...

Suppose that n independent observations are drawn from a multivariate normal distribution Np([mu],[Sigma]) with both mean vector [mu] and covariance matrix [Sigma] unknown. We consider the problem of estimating the precision matrix [Sigma]-1 under the squared loss . It is well known that the...

In this paper, the reference prior is developed for a truncated model with boundaries of support as two functions of an unknown parameter. It generalizes the result obtained in a recent paper by Berger et al. (2009), in which a rigorous definition of reference priors was proposed and the prior...

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...

The existence of the posterior distribution for one-way random effect probit models has been investigated when the uniform prior is applied to the overall mean and a class of noninformative priors are applied to the variance parameter. The sufficient conditions to ensure the propriety of the...