Mathematical Sciences: Computers for Statistical Research

本项目将研究多元线性回归和非线性回归的稳健回归程序。在第一种情况下，将开发出精确计算最小二乘估计中值的方法。将理论和计算推广到任意截尾的情形，并用Bootstrap方法生成置信度区间。在非线性回归的情况下，该项目将专注于确定MM-估计的稳健性，该估计已被证明在线性情况下是稳健的。预测通常是使用回归函数从数据计算出来的，回归函数将感兴趣的观察值与其他特征或属性的值联系起来。用于推导回归函数本身的传统计算很容易受到相当罕见但非常异常的单个数据点(离群值)的影响。更稳健的替代方法可以减少个别异常或奇怪数据点的影响；因此，这些方法应该能给出更稳定的预测。

This project will examine robust regression procedures for multiple linear regression and for nonlinear regression. In the first case, methods will be developed for the exact computations of least median of squares estimators. The theory and computation will be extended to the case when responses are arbitrarily censored; and bootstrap methods will be used to generate confidence intervals. In the case of nonlinear regression, the project will focus on determining the robustness of MM-estimation, which has been shown to be robust in the linear case. Predictions are often calculated from data using regression functions, which relate the value of the observation of interest to values of other features or attributes. Traditional computations used to derive the regression function itself are vulnerable to fairly rare but quite aberrant single data points (outliers). More robust alternative methods reduce the impact of individual unusual or bizarre data points; hence these methods should give more stable predictions.