Abstract:
Mixed models have been widely used to model data from experiments which have fixed and random
factors. Often there is interest in the estimation of fixed effects and variance components. The likelihood
procedure is a general technique that has been applied to such problems. This procedure can be
computationally difficult, as iterative algorithms are needed to solve for estimators that satisfy the
likelihood equations. Previous research has been done to identify conditions under which there exists an
explicit linear estimator for the full fixed effect vector or for the full variance component vector.
This thesis will examine explicit linear estimation in mixed models. The previous results will be
extended to explicit linear estimation of a linear combination of the fixed effects or of a linear
combination of the variance components. Specific results for the existence of an explicit linear estimator
for a subvector of the full fixed effect vector or a subvector of the full variance component vector will also be presented.
The results of the thesis will be demonstrated using various models encountered in the experimental
design setting. Applications will also be presented which include interpreting iterative procedures to solve
for the estimators, saving computer time in profile likelihood calculations for fixed effects, and uniformly
minimum variance unbiased estimation.
