The thesis studies determinants and adjustment paths of the people's weight from the view point of rational behavior.It followes the research approach of Becker and Murphy (1988), makes use of the utility function from Levy (2002), and corporates a budget constraint so as to establish an optimal control model for food consumption and weight, and to find out the relationship between them. Negative correlations are found between the steady-state weight and food prices, basal metabolic rate, and time discount rate.Positive correlations are found between the steady-state weight and income, marginal utility of food, and desirable weight. There is a tendancy to guide the actual steady-state weight to a much higher fluctuation margin than that of the desirable weight.In the dynamic analysis, it is also found that, regardless of an increase or decrease of the steady-state weight, both directions of adjustment show that the process of food consumption is always ``overshooting."In other words, when the steady-state weight becomes heavier (lighter), consumers first increase (decrease) their food consumption substantially. And, as the time goes by, there is a gradual decrease (increase) in food consumption owing to the fact that the food consumption is still higher (lower) than what is required for metabolism of the body that makes the weight getting to increase (decrease) till the new equilibrium is arrived.

Receiver Operating Characteristic (ROC) curves are often used to evaluate the prognostic performance of a continuous biomarker. In a previous research, a non-parametric ROC approach was introduced to compare two biomarkers with repeated measurements. An asymptotically normal statistic, which contains the subject-specific weights, was developed to estimate the areas under the ROC curve of biomarkers. Although two weighting schemes were suggested to be optimal when the within subject correlation is 1 or 0 by the previous study, the universal optimal weight was not determined. We modify this asymptotical statistic to compare AUCs between two correlated groups and propose a solution to weight optimization in non-parametric AUCs comparison to improve the efficiency of the estimator. It is demonstrated how the Lagrange multiplier can be used as a strategy for finding the weights which minimize the variance function subject to constraints. We show substantial gains of efficiency by using the novel weighting scheme when the correlation within group is high, the correlation between groups is high, and/or the disease incidence is small, which is the case for many longitudinal matched case-control studies. An illustrative example is presented to apply the proposed methodology to a thyroid function dataset. Simulation results suggest that the optimal weight performs well with a sample size as small as 50 per group.

In this thesis, we deal with finite Gibbs point processes, especially the processes with densities with respect to a Poisson point process. The main aim of this work is to investigate a four-parametric marked point process of circular discs in three dimensions with two and three way point interactions. In the second chapter, our goal is to simulate such a process. For that purpose, the birth- death Metropolis-Hastings algorithm is presented including theoretical results. After that, the algorithm is applied on the disc process and numerical results for different choices of parameters are presented. The third chapter consists of two approaches for the estimation of parameters. First is the Takacs-Fiksel estimation procedure with a choice of weight functions as the derivatives of pseudolikelihood. The second one is the estimation procedure aiming for the optimal choice of weight functions for the estimation in order to provide better quality estimates. The theoretical background for both of these approaches is derived as well as detailed calculations for the disc process. The numerical results for both methods are presented as well as their comparison. 1