This paper investigates the efficiencies of several generalized least squares estimators (GLSEs) in terms of the covariance matrix. Two models are analyzed: a seemingly unrelated regression model and a heteroscedastic model. In both models, we define a class of unbiased GLSEs and show that their...

When two groups are present, they are said to form an allometric model, if one group is the extension of the other group along the main axis of variation. The model is widely used in the context of principal component analysis, especially for the description of growth processes of creatures. In...

This paper complements the results of Tong (Ann. Statist. 17 (1989) 429), Shaked and Tong (Ann. Statist. 20 (1992) 614) and Eaton (in: Stochastic Inequalities, IMS Lecture Notes Monograph Series, Vol. 22, 1993, 76) by deriving some monotonicity results associated with intra-inter-class...

This paper presents a generalization of Rao's covariance structure. In a general linear regression model, we classify the error covariance structure into several categories and investigate the efficiency of the ordinary least squares estimator (OLSE) relative to the Gauss-Markov estimator (GME)....

In a seemingly unrelated regression model with p([greater-or-equal, slanted]2) equations, this paper considers the problem of testing independence of equations against a one-sided alternative hypothesis. The power functions of invariant tests are evaluated and the locally most mean powerful...

In this paper, first we make a maximal extension of the well-known Gauss-Markov Theorem (GMT) in its linear framework. In particular, the maximal class of distributions of error term for which the GMT holds is derived. Second, we establish a nonlinear version of the maximal GMT and describe some...

A set of n-principal points of a distribution is defined as a set of n points that optimally represent the distribution in terms of mean squared distance. It provides an optimal n-point-approximation of the distribution. However, it is in general difficult to find a set of principal points of a...