Direct Products and Linear Models for Complete Factorial Tables

Abstract

Direct products are used in some problems involving balanced factorial models for analysis of variance. Problems considered include demonstration that least squares estimators are minimum variance unbiased linear estimators when mixed models are considered, determination of the covariance structure of lest squares estimators, calculation of expected values of sums of squares and mean squares, and determination of the distribution of sums of squares and least squares estimators under the normality assumption.