Ellenberg J H
Biometrics. 1976 Sep;32(3):637-45.
Several authors have considered the problem of detection of outliers from the general linear model Y = Xbeta + mu. Ellenberg [1973] among others, has advocated use of a detection method which involves examination of the set of internally standardized least squares residuals. Mickey [1974] and Snedecor and Cochran [1968], apparently concerned about the usefulness of an outlier detection method which is based on residual estimates that themselves are biassed by the presence of the outlier, have proposed two other alternatives. It is shown that the three approaches are exactly equivalent. A detection procedure is described which uses as its test statistic the maximum of the internally standardized least squares residuals, and upper and lower bounds for the percentage points of the test statistic are given by Bonferroni inequalities. The computations required to obtain these approximate percentage points are illustrated in a numerical example. Finally, a brief simulation study of the performance of the procedure illustrates that the power of the test can be influenced by the position of the outlier vis-a-vis the structure of the design matrix X.
几位作者已经考虑了从一般线性模型Y = Xβ + μ中检测异常值的问题。埃伦伯格[1973]等人主张使用一种检测方法，该方法涉及检查内部标准化最小二乘残差集。米奇[1974]以及斯内德科尔和科克伦[1968]显然担心一种异常值检测方法的有效性，该方法基于本身会因异常值的存在而产生偏差的残差估计，他们提出了另外两种替代方法。结果表明，这三种方法完全等效。描述了一种检测程序，该程序使用内部标准化最小二乘残差的最大值作为其检验统计量，并通过邦费罗尼不等式给出检验统计量百分点的上下界。在一个数值示例中说明了获得这些近似百分点所需的计算。最后，对该程序性能的简要模拟研究表明，检验的功效会受到异常值相对于设计矩阵X结构的位置的影响。
