U.S.-Belgium Cooperative Research: Bandwidth Selection and Construction of Confidence Bands in Nonparametric Regression

该奖项将支持北卡罗来纳大学教堂山分校的James Marron博士和比利时鲁汶天主教大学的Wolfgang Hardle教授在统计和概率方面的合作研究。本研究的目的是研究加性多元回归模型的带宽选择和置信带/误差条的构建。本研究涉及非参数回归，特别是在多变量情况下。要解决的两个主要问题是平滑参数（即带宽选择）和基于数据的估计器精度评估（本着置信区间的精神）。非参数回归提供了一个强大的工具，在没有被广泛接受的模型可用的情况下，或者在对给定模型的适当性有一些怀疑的情况下，提供洞察力。在实际应用中，最需要的两个改进是一种真正可靠的带宽选择方法，以及评估估计器可变性的方法。Drs。Marron和Hardle在过去的联合研究中有着良好的记录，这将有利于这次拟议的合作。

This award will support collaborative research in statistics and probability between Dr. James Marron, University of North Carolina at Chapel Hill, and Professor Wolfgang Hardle, Catholic University of Louvain, Belgium. The objective of the research is to study bandwidth selection and construction of confidence bands/error bars for additive multivariate regression models The proposed research concerns nonparametric regression, especially in the multivariate case. The two main problems to be addressed are smoothing parameters (i.e. bandwidth selection) and data based assessment of the accuracy of estimators (in the spirit of confidence intervals). Non- parametric regression provides a powerful tool for providing insights in situations where no widely accepted model is available, or where there is some doubt concerning the appropriateness of a given model. For practical applications, the two improvements most needed are a really reliable method of bandwidth selection, and a means of assessing the variability of the estimator. Both Drs. Marron and Hardle have a strong record of past joint research, which will be of benefit to this proposed collaboration.