最小二乘回归中的局部影响评价  

ASSESSING LOCAL INFLUENCE IN LEAST SQUARE REGRESSION

作　　者：吴志新[1] 石磊[2] 张无畏[3] 

机构地区：[1]楚雄师专电大 [2]云南大学统计系 [3]楚雄师专经济系

出　　处：《楚雄师范学院学报》1999年第3期50-55,共6页Journal of Chuxiong Normal University

摘　　要：本文就最小二乘回归模型，利用广义影响函数及广义COOK统计量[1]的方法，研究了模型中的某一部份发生微小扰动时相关统计量的局部影响评价问题。这一方法不依赖于模型的似然假设。所得结果与COOK[2]的方法进行了比较。我们研究并导出了回归系数的最小二乘数估计，预测估计及参数函数估计的局部影响度量，并与数据删除法及导数法进行了比较，最后，用两个实例进行了说明。In this paper, the generalized influence function of a vector - valued statistic is defined under a minor perturbation scheme and norm - generalized Cook Statistic is used to assess the Iocal chang caused by small perturbation on the concerned statistic. This method, with weaker reliance on likelihood assumption, is commpared to Cook's local influence based on normal curvature. In the forwork of linear least square regression, the local effect of small perturbations on the LSE of unknown parameter and prediction are studien, and these results are compared to that of case deletion. Finally, two examples are used for illustration.

关 键 词：扰动模式 广义影响函数 广义COOK统计量 最小二乘回归 局部影响 

分 类 号：O212[理学—概率论与数理统计]