This dissertation examines limiting efficiencies of
quadratic unbiased estimators for the variance in the
two variance component mixed model. The set of
quadratic unbiased estimators considered includes the
minimal complete class. A theorem is proved which shows
that, in certain cases, a relatively simple expression
converges to the same value...
This dissertation is concerned with hypothesis testing for
fixed effects in mixed linear models. Our primary emphasis is on
mixed models when the class of covariance matrices has what we
call a rich linear structure. Such models include mixed ANOVA
models and regression models with heteroscedastic variances. For
We describe a general finite-dimensional inner product space setting for studying the characterization of admissible linear estimators. We extend the results of LaMotte (1982) and derive necessary and sufficient conditions for an estimator to be admissible among an arbitrary affine set of linear estimators when they are compared using quadratic...
Measuring the source and magnitude of components of variation has important
applications in industrial, environmental and biological studies. This thesis considers
the problem of constructing confidence intervals for variance components in Gaussian
mixed linear models. A number of methods based on the usual ANOVA mean squares
have been proposed for...
Testing main effects and interaction effects in factorial designs are basic content
in statistics textbooks and widely used in various fields. In balanced designs there
is general agreement on the appropriate main effect and interaction sums of
squares and these are typically displayed in an analysis of variance (ANOVA). A...