This research will cover two major topics, inference problems when data are corrupted by errors of measurement and inequalities for martingale type sequences of random variables. The first topic focusses primarily on instrumental variable estimation in generalized linear and nonlinear measurement error regression models. Inference methods to be studied include maximum likelihood, conditional likelihood and quasilikelihood estimation based on approximate data models. The second topic involves comparison methods for tangent sequences of martingale differences. Special attention will be given to problems involving domination of martingales by martingales with conditionally independent increments. Specific topics to be investigated include norm inequalities, exponential inequalities and stability properties for martingale type sequences. This research is focussed on two different topics. The first area involves problems of inference and data analysis when data are not measured precisely. The second topic is concerned with comparison methods for sums of random variables. These methods provide a better understanding of modern probability theory.
