Mathematical Sciences: Nonparametric Curve Estimation

这个项目讨论了平滑方法在非参数曲线估计中的理论和应用。这里的重点是带宽选择与精确的风险计算和定性平滑和检查的优越性局部多项式平滑更常用的方法。对于局部多项式平滑器，该项目将解决边界效应、百分位数回归和鲁棒化、变量拟合顺序、拟合优度测试和局部加权似然等问题。非参数曲线估计中的平滑方法是一种灵活而有力的数据分析方法，在没有精确甚至有用模型的复杂情况下特别有用。例如，在经济学、动物学和市场营销等领域都会出现这样的问题。平滑方法的有效实际实施需要对其性质的分析理解。

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.