Mathematical Sciences: Some Problems in Nonparametric Regression

数学科学：非参数回归中的一些问题

• 批准号: 8902576
• 负责人: Randall Eubank
• 金额: $ 4.24万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1992-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902576&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Some; Problems; Nonparametric

Eubank proposes to examine a number of problems in nonparametric regression. One of the most interesting is the problem of robust spline smoothing. The typical spline estimator of a regression function is found by minimizing a sum of squared errors plus a penalty function. However the sum of squared errors is highly sensitive to outliers. By substituting absolute error for squared error (or another appropriate function of the error) one can make the estimator more robust to outliers. Eubanks will examine the effect of incorporating and estimating a scale factor for the error terms in these more appropriate and general functions of the errors. He will also examine jackknife confidence intervals for the underlying regression function. These nonparametric regression models will also be applied to the traditional analysis of variance, analysis of covariance and intra-class regression models. Another problem he will address is the incorporation of the covariance structure of order statistics in the estimation of quantile functions and their densities. The problem of relating two variables (such as height and weight) for pairs of observations on individuals is addressed by nonparametric regression. Finding a functional relationship between the two variables is made considerably harder if some information is miscoded or extremely unusual individuals are included in the data. Eubank will investigate methods of finding functional relationships that will be less sensitive to outliers in the sample and more representative of the whole population.

尤班克建议审查一些问题， 非参数回归 其中最有趣的是 鲁棒样条平滑问题 典型的spline 回归函数的估计量是通过最小化和 平方误差加上一个惩罚函数 然而， 平方误差对异常值高度敏感。 通过 用绝对误差代替平方误差（或另一种 误差的适当函数），可以使估计器 对异常值更稳健。 尤班克斯将研究 合并并估计所述误差项的比例因子 在这些更适当和一般的功能的错误。 他还将检查jackknife置信区间， 底层回归函数。 这些非参数回归 模型也将应用于传统的分析， 方差、协方差分析和类内回归 模型 他将解决的另一个问题是 中顺序统计量的协方差结构 分位数函数及其密度的估计。 将两个变量（如身高和 权）对个人的意见是解决 非参数回归 寻找功能关系 两个变量之间的关系变得相当困难， 信息被错误编码或极端不寻常的个人被 包括在数据中。 尤班克将研究 找到对以下因素不太敏感的功能关系 样本中的离群值，更能代表整体 人口