发表机构
Alexandria University（亚历山大大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种线性回归异方差性检验方法，通过排序分组比较误差尺度，精确零分布且抗离群值，在多种模拟设置中功效优于现有检验，并支持沿时间变化的方差检测。
AI 中文摘要
线性回归中的异方差性检验在三种情况下会失去其水平或功效：当数据包含离群值时，当方差不是单调变化时，以及当方差沿回归变量之外的变量（如时间）变化时。所提出的检验方法按任意选择的变量对观测值进行排序，将其分成三个相等部分，在每一部分中拟合回归，并比较最大与最小误差尺度。使用最小二乘拟合和正态误差时，该比率精确地服从具有三组的Hartley最大F分布。使用最小截尾平方拟合时，该比率能抵抗沿排序方向分布的离群值。其平方近似为具有有效自由度的最大F比率，我们通过截尾方差的影响函数以闭式形式推导出其极限。一项因子模拟覆盖了方差形状、排序变量、回归变量数量、污染和样本量的72种设置。稳健检验的平均规模调整功效最高，为67%，而次优检验为45%；当方差沿回归变量变化时（所有检验均被告知此情况），它在离群值筛选后优于White检验，为67%对56%。对于重尾t3误差，其优势类似，为64%对35%。与基于回归变量构建的检验不同，它能够跟踪沿时间变化的方差，并识别方差变化的数据部分。根据其描述实现的两个已发表的Goldfeld-Quandt检验的稳健版本未能保持其名义水平。R包KOTORY实现了这些方法。
英文摘要
Tests for heteroscedasticity in linear regression lose their level or power in three situations: when the data contain outliers, when the variance is not monotone, and when it changes along a variable outside the regressors, such as time. The proposed tests sort the observations by any chosen variable, split them into three equal parts, fit the regression in each part and compare the largest with the smallest error scale. With least squares fits and normal errors, the ratio follows Hartley's maximum F distribution with three groups exactly. With least trimmed squares fits, the ratio resists outliers spread along the ordering. Its square is approximately a maximum F ratio with effective degrees of freedom, whose limit we derive in closed form from the influence function of the trimmed variance. A factorial simulation covered 72 settings of variance shape, ordering variable, number of regressors, contamination and sample size. The robust test had the highest mean size-adjusted power, 67%, against 45% for the next test; when the variance changed along a regressor, which all tests were given, it led White's test after an outlier screen, 67% against 56%. With heavy-tailed t3 errors its lead was similar, 64% against 35%. Unlike the tests built on the regressors, it can follow a variance changing along time, and it identifies the part of the data where the variance changes. Two published robust versions of the Goldfeld-Quandt test, as implemented from their descriptions, did not hold their nominal level. The R package KOTORY implements the methods.
Comments28 pages, 7 figures, 5 tables; Online Resource 1 (3 pages) is included as an ancillary file. Code and per-replication results: https://doi.org/10.5281/zenodo.23038198 ; R package KOTORY: https://github.com/ebrahimkhaled/KOTORY
