Mathematical Sciences: Nonparametric Curve Estimation

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This project addresses the theory and application of smoothing methods in nonparametric curve estimation. The focus here is on bandwidth selection with exact risk calculation and qualitative smoothing and on an examination of the superiority of local polynomial smoothers to more commonly used methods. For local polynomial smoothers, this project will address issues of boundary effects, percentile regression and robustification, variable order of fit, goodness-of-fit testing and local weighted likelihood. Smoothing methods in nonparametric curve estimation constitute a flexible and powerful approach to data analysis which is of particular use in complicated situations where an exact or even useful model is unavailable. Such problems arise, for example, in economics, zoology, and marketing among other areas.Effective practical implementation of smoothing methods requires analytic understanding of their properties.