Mixed Model Variance Analysis with Normal Error and Possibly Non-Normal Other Random Effects: Part II: The Multivariate Case

Abstract

The present paper is a continuation of another with similar title and the same overall objectives--confidence bounds on appropriate measures of the dispersion of the distribution from which random (block) effects are drawn in an experiment where fixed (treatment) effects are also under investigation. Specifically, confidence bounds are obtained on the maximum and minimum characteristic roots of the variance matrix of the block effects when the latter are assumed to come from a $p$-variate normal distribution (without the assumption made in [1], [5] that this variance matrix is proportional to that of the error). When the random block effects are not assumed to be normal, consideration is given to the approximation of an unknown multivariate distribution by means of marginal and conditional quantiles. Then for a rather restricted bivariate case, simultaneous confidence bounds are found for the two interquartile ranges. Since the ideas and notation of the first paper are presupposed by this one, much duplication is avoided by reference to appropriate sections or steps in the previous article. To facilitate such reference, the numbering is consecutive through both parts.