This research examines three classes of statistical models in common use. The first topic is aliasing in models for the covariance function of random processes and arrays. The second topic involves the further use of higher-order cumulants and Edgeworth expansions to study the behaviour of estimators and tests in variance component analysis. The final topic is the method of residual or restricted maximum likelihood estimation of variance and covariance parameters. This research in statistics will impact the areas of spectral analysis, analysis of variance, and the users of the classical random effects and mixed linear models in fields such as agriculture, plant and human genetics, psychology and manufacturing.
