随机约束Liu回归的局部影响分析

Local Influence Analysis for the Liu Regression under Stochastic Linear Restrictions

摘要: 在进行回归诊断时，影响点的检测一直是统计学者们研究的一个热点问题，而大多数情况下变量之间会存在自相关性即复共线性，再利用普通最小二乘估计进行影响点的检测会掩盖或掩没一些影响点，得到某些误导性结论。因此，本文考虑利用随机约束Liu估计克服数据间存在复共线时对检测带来的影响，在随机约束Liu回归模型下通过Cook似然距离和Tsai、Billor和Loynes (TBL)的另一种似然距离两种局部影响分析方法来检测影响点，分别在三种扰动模型下得到了影响矩阵、影响曲率和梯度所需的计算公式。最后，通过Longley数据集说明了两种方法都能检测影响点。

Abstract: In regression diagnosis, the detection of influence points has always been a hot issue studied by statisticians. In most cases, there will be autocorrelation between variables, namely complex collinearity, and the detection of influence points by using ordinary least square estimation will cover up or conceal some influence points and get some misleading conclusions. Therefore, in this paper, we consider using random constrained Liu estimation to overcome the influence of complex collinear data on detection. Under the random constrained Liu regression model, two local impact analysis methods, Cook likelihood distance and another likelihood distance of Tsai, Billor and Loynes (TBL), are used to detect the influence points. The formulas of influence matrix, influence curvature and gradient are obtained under three disturbance models. Finally, Longley data set shows that both methods can detect influence points.