Multivariate Variance Components Model Research Articles

Least Squares Estimation of Covariance Matrices in Balanced Multivariate Variance Components Models

Abstract The problem of estimating covariance matrices in balanced multivariate variance components models is discussed. As with univariate models, it is possible for the traditional estimators, based on differences of the mean square matrices, to produce estimates that are outside the parameter space. In fact, in many cases it is extremely likely that traditional estimates of the covariance matrices will not be nonnegative definite (nnd). In this article we develop an iterative estimation procedure, satisfying a least squares criterion, that is guaranteed to produce nnd estimates of the covariance matrices, discuss the speed of convergence, and provide an example to show how the estimates change.

Maximum Likelihood Estimation of a Set of Covariance Matrices Under Lowner Order Restrictions with Applications to Balanced Multivariate Variance Components Models

The problem of maximum likelihood estimation of Lowner ordered covariance matrices is considered. It is shown that a dual formulation of this problem is tractable and important in its own right. The interplay between the primal and dual problems suggests a general algorithm for computing the solutions to these problems. This algorithm has application to some estimation problems in balanced multivariate variance components models. The speed of convergence is also discussed for the variance components models.

A note on the equivalence of specification tests in the two-factor multivariate variance components model

This note offers a generalization of Hausman and Taylor's equivalence of specification tests in the single-equation variance (error) components model to the two-factor multivariate variance components case. The relationship between the specification tests and the hypothesis test in the model proposed by Mundlak is also discussed.

On a result of roy and Gnanadesikan concerning multivariete variance components

Roy and Gnanadesikan [5] showed that inference for a general multivariate variance components model may be carried out using the standard multivariateF distribution under certain condtions. It is shown in this note that the theory of zonal polynomials, and their extension by the author to invariant polynomials in two matrix arguments, provide a concise approach to the derivation of these conditions. Relevant distributions are also derived for the general case.

On the Analysis of Variance Test in Multivariate Variance Components Model

On the Analysis of Variance Test in Multivariate Variance Components Model