线性回归中常用估计影响分析的统一方法

A Unified Method for Influence Analysis of Some Estimates in Multivariate Linear Regression

在多元线性回归模型中，对参数的几种常见估计给出了统一的表达式，进而讨论了一组试验数据对参数估计的影响，把这几种常见估计的影响分析进行了统一处理。利用经验影响函数的某种国数考虑影响问题，给出了异常点、高杠杆点与强影响点之间的关系，从而把文献［３］的结果推广到多元的情形，同时改进了文献［２］的一个结果，给出了判别统计量的分布。

This paper gives aunified expression for several estimates in multivariate linear regression .Furthermore, the influence of a set of datea on the parameter estimate is discudded and a unified method for analysing influence of this estimate is given .By considering the influence problem by means of a function fo the empirical influence function,the relation between outlier,high leverage case and influence case is presented to gen erate the results of [3]to multivariate case and improve one of the results of [2].