Mathematical Sciences: Computers for Statistical Research

本项目将研究稳健的回归程序， 多元线性回归和非线性回归。 在 第一种情况下，方法将开发的精确计算 最小二乘估计的最小中位数。 理论与 计算将扩展到响应时的情况下， 任意删失;自助方法将用于 生成置信区间。 在非线性的情况下， 回归，该项目将侧重于确定鲁棒性 的MM估计，这已被证明是强大的线性 案子 预测通常使用回归从数据计算 函数，这些函数将感兴趣的观测值 其他特征或属性的值。 传统 用于导出回归函数本身的计算是 容易受到相当罕见但相当异常的单一数据点的影响 （离群值）。 更稳健的替代方法可减少 个别不寻常或奇异的数据点;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.