Mathematical Sciences: Nonparametric Regression for VarianceFunction Estimation and Surface Fitting

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The principal investigator will work on two major problems in the area of nonparametric regression: multivariate smoothing and variance function estimation. For the smoothing of surfaces, without any restrictions like additivity of the function or other assumptions to reduce dimensionality, an approach based on mixtures between an orthogonal series method using ultraspherical expansions and kernel estimators is to be developed. The main problems to be analyzed are the choice of bandwidths, boundary effects and their treatment, associated questions of uniform convergence, the estimation of isoklines and the development of fast and efficient algorithms. In his work on nonparametric variance function estimation he will develop methods for constructing confidence and prediction intervals of the variance. The nonparametric analysis of curve data has found considerable interest among statisticians facing applied problems from longitudinal biomedical studies as well as geophysical and environmental spatial data. The principal investigator will work on two specific problems in this area: surface fitting and variance function estimation.