When the maximum likelihood estimator is computationally inconvenient, covariate and Newton–Raphson adjustment often provide algebraically explicit yet still asymptotically efficient estimators. The bivariate normal correlation coefficient with known variances is used to show that these...

We consider normal [reverse not equivalent] Gaussian seemingly unrelated regressions (SUR) with incomplete data (ID). Imposing a natural minimal set of conditional independence constraints, we find a restricted SUR/ID model whose likelihood function and parameter space factor into the product of...

Consider s+1 univariate normal populations with common variance [sigma]2 and means [mu]i, i=0,1,...,s, constrained by the tree-order restrictions [mu]i[greater-or-equal, slanted][mu]0, i=1,2,...,s. For certain sequences [mu]0,[mu]1,... the maximum likelihood-based estimator (MLBE) of [mu]0...

Lattice conditional independence (LCI) models (Anderson and Perlman, 1991. Statist. Probab. Lett. 12, 465-486; 1993 Ann. Statist. 21, 1318-1358) can be applied to the analysis of missing data problems with non-monotone missing patterns. Closed-form maximum likelihood estimates can always be...

A multivariate normal statistical model defined by the Markov properties determined by an acyclic digraph admits a recursive factorization of its likelihood function (LF) into the product of conditional LFs, each factor having the form of a classical multivariate linear regression model...

Let X ~ Np(0, [Sigma]), the p-variate normal distribution with mean 0 and positive definite covariance matrix [Sigma]. Anderson (1955) showed that if [Sigma]2 - [Sigma]1 is positive semidefinite then P[Sigma]1(C) [greater-or-equal, slanted] P[Sigma]2(C) for every centrally symmetric (- C = C)...