扰动模型参数估计的影响度量

本文从均方误差角度，引入了一种新的影响度量统计量ＭＥ（ｉ），讨论了ＧａｕｓｓＭａｒｋｏｖ模型（Ｙ，ｘβ，σ２Ｉｎ）在剔除数据点（ｙｉ，ｘｉ）的扰动下对ＬＳ估计及预测的影响问题，并在ＭＥｉ与影响分析中异常点，强影响点常用的度量统计量之间建立了一定的联系，得到了一致的结论和判断效果。进而在引入原模型误差方至σ２的一种新的无偏估计σ２的基础上，通过ＭＥｉ把影响分析的讨论与回归模型选择的ＰＲＥＳＳ准则建立了一定的联系．以一种新的统计解释对回归诊断中数据的影响分析和模型适宜性给以了刻划。最后以一个简单的计算实例，显示了这种刻划的合理性及与常用判定准则的一致性。

Influence Measure of the Parameter Estimation in the Perturbation Regression Model

In regression, it is of interest detct anomalous observations that exert anunduly large influence on the least squares analysis. Some influence easures.have been discussed. But all the measures dont't discuss the linear-regressionmodel, when a severable data point case is deletion of influential observations.Westudy the relation ME(i) for the deection of influential observations Westudy the relation between the influence analysis and Allen's PRESSS principle in the choice of regression modeds, and give some interestingresults.