论文标题
关于回归的删除诊断统计量
On deletion diagnostic statistic in regression
论文作者
论文摘要
由于案例缺失而导致的回归系数载体的最小二乘估计量（LSE）的变化通常用于研究观察结果对LSE的影响。使用Moore-Penrose的变化归量化，使用了LSE变化的协方差矩阵的倒数。这种归一化事实证明是内部学生剩余的平方。结果表明，除单个情况外，库克距离的分子项一般没有卡方分布。关于定义库克距离的缩放矩阵选择的不适当性的精心解释。通过反映由于案例删除而反映LSE中变化的分布属性，这是一种新的诊断措施，这是标量的。给出了三个数字示例以进行插图。
The change in the least squares estimator (LSE) of a vector of regression coefficients due to a case deletion is often used for investigating the influence of an observation on the LSE. A normalization of the change in the LSE using the Moore-Penrose inverse of the covariance matrix of the change in the LSE is derived. This normalization turns out to be a square of the internally studentized residual. It is shown that the numerator term of Cook's distance does not in general have a chi-squared distribution except for a single case. An elaborate explanation about the inappropriateness of the choice of a scaling matrix defining Cook's distance is given. By reflecting a distributional property of the change in the LSE due to a case deletion, a new diagnostic measure that is a scalar is suggested. Three numerical examples are given for illustration.
