The variability among data may have quite complex structure and the splitting of variation into its individual components is important in many areas of applications. In particular, the study of variation through a class of linear models known as random and mixed models is a central topic in statistics with wide ramifications in both theory and applications. Sometimes these models are called components of variance models since the interest in the model lies in investigating the variances of the effects of factor levels which are assumed to be randomly selected from a large population of levels. These variances are also known as variance components since the total variance can be expressed as the sum of these variances and the error variance. Knowledge of the variance components, i.e., the information on the relative importance and magnitude of the sources of variability in the data is of critical importance in many problems since the isolation of the total variance into the individual components of variance would result in the physical elimination of the sources of variability in question.

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A bibliography on variance components an introduction and an update: 1984-2002

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Bibliography of Multivariate Procedures for Unbalanced Data

Three HENDERSON'S Methods of estimating the variance components are generalized from one to p variables using a compact matrix notation. These results are obtained using a generalized Kronecker product of matrices, generalized trace of order p and a generalized quadratic form.

M. T. Wesolowska-Janczarek

Papers

Estimation of Covariance Matrices in Unbalanced Random and Mixed Multivariate Models