In the problem of testing the median using a random sample from a
certain distribution, and if no other parametric family is suggested,
the t-test is known to be the optimal procedure when this distribution
is normal. If the sample appears to be non-normal, one has the choice
either to...
This dissertation considers two approaches for testing hypotheses in
unbalanced mixed linear models. The first approach is to construct a design with
some type of structure or "partial" balance, so that some of the optimal properties of
a completely balanced design hold. It is shown that for a particular type...
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,...
Missing data can lead to biased and inefficient estimation if the missing mechanism is not taken into account in the analysis. In this dissertation we propose two estimators that, under fairly general conditions, are asymptotically unbiased. The first proposed estimator assume the data are missing at random (MAR) and does...
For data following a balanced mixed Anova model, the standard Anova method typically leads to exact F tests of the usual hypotheses about fixed effects. However, for most unbalanced designs with most hypotheses, the Anova method does not produce exact tests, and approximate methods are needed. One approach to approximate...
Statisticians often focus on sampling or experimental design and data analysis while paying less attention to how the response is measured. However, the ideas of statistics may be applied to measurement problems with fruitful results. By examining the errors of measured responses, we may gain insight into the limitations of...