基于MM算法的LAD回归的影响分析  

Influence analysis of LAD regression based on MM algorithm

作　　者：徐亮[1] 周影辉[1] 韦博成[1] 

机构地区：[1]东南大学应用数学系,江苏南京210096

出　　处：《高校应用数学学报（A辑）》2007年第1期48-58,共11页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(10371016)

摘　　要：基于Hunter and Lange(2000)提出的MM迭代算法,构造了一个代替L1目标函数的新的目标函数Qε(ββk);在此基础上研究了非线性LAD回归影响分析的若干问题.基于新的目标函数和MM迭代算法,证明了LAD回归模型中数据删除模型和均值漂移模型参数估计的等价性定理,并提出了一种新的影响度量.最后,几个数据实例说明了方法的有效性.Least absolute deviation （LAD） regression, i.e. L1 regression, is more resistant to the outliers in the response variable than the least-squares （LS） regression, but is relatively sensitive to outlying observations in explanatory variables. However, some but few attention has been contributed to the influence assessment for LAD regression because of the complexity of the objective function in LAD reression. This paper creates a new objective function, i.e. Qk（β｜β^k）, instead of LI objective function based on the MM iterative algorithm proposed by Hunter and Lange （2000）. On the basis of the new objective function and MM iterative algorithm, the paper proves that the estimates of the case deletion model （CDM） and the mean shift outlier model （MSOM） are equal in linear and nonlinear LAD regression models, and proposes a new influence measure. In the end, some real examples are given to illustrate the use of this method.

关 键 词：LAD回归 MM算法 影响分析 异常点 

分 类 号：O212.1[理学—概率论与数理统计]