Mueller In this research, statistical models which contain parametric, smooth and discontinuous components are developed and applied to problems which involve high-dimensional regression, samples of curves as observations, or change-points and jump discontinuities. These models are motivated by scientific problems including the longitudinal analysis of samples of cohorts of subjects, the analysis of spatial incidence data describing the spread of diseases, and the growth of children, where discontinuities may occur. This also includes models which incorporate the influence of covariates on a sample of response curves, and the construction of models with discontinuous elements in the context of segmentation of DNA sequences and of edge detection in image analysis. Methods for fitting the models are devised, which typically involve complex iterative algorithms using smoothing techniques, generalized linear models and estimating equations as building blocks. The properties of these methods are analyzed and they are applied to data pertaining to the scientific problems. This research contributes to the solution of major scientific problems by providing innovative statistical methods. One such problem is the mortality of the older segments of a population and what one can say about the aging process based on animal models, with potential impact on social security and health care in the 21st century. Sophisticated methods are needed in order to extract and combine the information on the observed survival of the individuals from many cohorts. Another problem is to describe and analyze the spatial spread of AIDS and of other epidemics as time passes. A third problem is the segmentation of DNA sequences which then may allow for association of the segments with biological functions. These and related problems can be put into the framework of the new statistical models which are developed in this research. The application of these models allows to gain important new insight s into fundamental scientific aspects of these complex problems.
