Mathematical Sciences: Advanced Methods in Semiparametric and Nonlinear Model Building

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This research project is to provide theoretical and advanced computational methods for linear and nonlinear model building in both a parametric and a semiparametric context, with both large and small data sets. Partial and interaction splines and combining the problems of non-Gaussian data, nonlinear observation functionals and apriori inequality constraints will be used in large scale multivariate semi-parametric model building. Part of the emphasis will be on sequential semiparametric model building techniques suitable for very large data sets with several concomitant variables. Certain model fitting problems in multivariate density estimation will also be considered, as will methods for approximating and displaying likelihood contours for nonlinear statistical models and the application of these techniques to the investigation of multiparameter interactions in several types of non-linear model formulations. This research is in the general area of semi-parametric statistical methods. Such methods incorporate fewer assumptions than embodied in pure parametric methods but retain critical aspects of their structure. Results with significance for both the statistical sciences community and the general science and engineering community are expected.