Doctor of Philosophy / Department of Statistics / Dallas E. Johnson / Over the years sampling and experimental design have developed independently with little mutual compatibility. However, many studies do (or should) involve both a sampling design and an experimental design. For example, a polluted site may be exhaustively partitioned into area plots, a random sample of plots selected, and the selected plots randomly assigned to three clean-up regimens. In this research the relationship between sampling design and experimental design is discussed and a basic review of each is given. An estimator that combines sampling and experimental design is presented and it's development explained. Properties of this estimator will be derived and some applications of the estimator will be examined. Finally, a simulation study comparing this estimator with the traditional estimator will be presented.

Title: Parameter Estimation under Two-phase Stratified and Cluster Sampling Author: Mgr. Michaela Šedová Department: Department of Probability and Mathematical Statistics Supervisor: Doc. Mgr. Michal Kulich, Ph.D. Abstract: In this thesis we present methods of parameter estimation under two-phase stratified and cluster sampling. In contrast to classical sampling theory, we do not deal with finite population parameters, but focus on model parameter inference, where the ob- servations in a population are considered to be realisations of a random variable. However, we consider the sampling schemes used, and thus we incorporate much of survey sampling theory. Therefore, the presented methods of the parameter estimation can be understood as a combination of the two approaches. For both sampling schemes, we deal with the concept where the population is considered to be the first-phase sample, from which a sub- sample is drawn in the second phase. The target variable is then observed only for the subsampled subjects. We present the mean value estimation, including the statistical prop- erties of the estimator, and show how this estimation can be improved if some auxiliary information, correlated with the target variable, is observed for the whole population. We extend the method to the regression problem....