The generalized information criterion (GIC) proposed by Rao and Wu [A strongly consistent procedure for model selection in a regression problem, Biometrika 76 (1989) 369-374] is a generalization of Akaike's information criterion (AIC) and the Bayesian information criterion (BIC). In this paper,...

Minimax designs and maximin efficient designs for estimating the location-shift parameter of a parallel linear model with correlated dual responses over a symmetric compact design region are derived. A comparison of the behavior of efficiencies between the minimax and maximin efficient designs...

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...

This paper deals with the bias reduction of Akaike information criterion (AIC) for selecting variables in multivariate normal linear regression models when the true distribution of observation is an unknown nonnormal distribution. We propose a corrected version of AIC which is partially...

Linear regression models with vague concepts extend the classical single equation linear regression models by admitting observations in form of fuzzy subsets instead of real numbers. They have recently been introduced [cf. Krätschmer, Induktive statistik auf basis unscharfer meßkonzepte am...

The theory of Gaussian graphical models is a powerful tool for independence analysis between continuous variables. In this framework, various methods have been conceived to infer independence relations from data samples. However, most of them result in stepwise, deterministic, descent algorithms...

The formula of Faa di Bruno is used to calculate higher order derivatives of a composition of functions. In this paper, we first review the multivariate version due to Constantine and Savits [A multivariate Faa di Bruno formula with applications, Trans. AMS 348 (1996) 503-520]. We next derive...

We propose a new definition of the Neyman chi-square divergence between distributions. Based on convexity properties and duality, this version of the [chi]2 is well suited both for the classical applications of the [chi]2 for the analysis of contingency tables and for the statistical tests in...

Reduced-rank restrictions can add useful parsimony to coefficient matrices of multivariate models, but their use is limited by the daunting complexity of the methods and their theory. The present work takes the easy road, focusing on unifying themes and simplified methods. For Gaussian and...

This article completes and simplifies earlier results on the derivation of best linear, or affine, unbiased estimates in the general Gauss-Markov model with a singular dispersion matrix and additional restrictions under very general conditions. We provide the class of all linear representations...