Mathematical Sciences: Some Problems in Nonparametric Regression

数学科学：非参数回归中的一些问题

基本信息

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

项目摘要

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.

Eubank建议检查非参数回归中的许多问题。最有趣的之一是稳健的样条曲线平滑的问题。通过最小化平方错误和惩罚函数的总和，可以找到回归函数的典型样条估计器。但是，平方错误的总和对离群值高度敏感。通过将绝对误差替换为平方错误（或错误的另一个适当函数），可以使估算器更加与离群值更强大。 Eubanks将检查在这些错误的更合适和一般函数中纳入和估算错误项的比例因子的效果。他还将检查基础回归函数的小刀置信区间。这些非参数回归模型也将应用于传统的方差分析，协方差分析和类内回归模型。他将要解决的另一个问题是将秩序统计的协方差结构纳入分位数函数及其密度的估计。通过非参数回归解决了将两个变量（例如身高和体重）与个体的观测成对相关的问题。如果某些信息被错误编码或非常不寻常的个体包含在数据中，则发现两个变量之间的功能关系变得更加困难。 Eubank将研究发现功能关系的方法，这些功能关系对样本中的离群值和整个人群的代表性更大。