Mathematical Sciences: Smoothing Parameters and Model Selection

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The principal investigator will study the problems of smoothing parameter (bandwidth) selection for nonparametric models, and order selection for linear models. Nonparametric and linear models have been used extensively in many fields. Although there are many procedures available for selecting the bandwidth or the order, it is recognized that the classical selectors are subject to large sample variation, and thus may not be very useful in practice. Recently, using the technique of Fourier analysis, the investigator proposed some stabilized procedures to reduce the variation in selecting the bandwidth for kernel regression of density estimation. This project will follow the approach recently obtained by the investigator to study the bandwidth or order selection problems for several important cases, which include boundary effects, random design points, order selection for autoregressive processes, extraction of periodic components, point processes, and robust smoothers.