It is shown how Passing’s and Bablok’s robust regression method may be derived from the condition that Kendall’s correlation coefficient tau shall vanish upon a scaling and rotation of the data. If the ratio of the standard deviations of the regressands is known, a similar procedure leads to a robust alternative to Deming regression, which is known as the circular median of the doubled slope angle in the field of directional statistics. The derivation of the regression estimates from Kendall’s correlation coefficient makes it possible to give analytical estimates of the variances of the slope, intercept, and of the bias at medical decision point, which have not been available to date. Furthermore, it is shown that using Knight’s algorithm for the calculation of Kendall’s tau makes it possible to calculate the Passing–Bablok estimator in quasi-linear time. This makes it possible to calculate this estimator rapidly even for very large data sets. Examples with data from clinical medicine are also provided.

中文翻译：

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从肯德尔的tau推导Passing–Bablok回归

展示了如何根据肯德尔相关系数tau在数据缩放和旋转后消失的情况得出Passing和Bablok的鲁棒回归方法。如果已知回归数的标准偏差的比率，则类似的过程将导致替代Deming回归的可靠方法，这在定向统计领域中被称为加倍倾斜角的圆中值。根据肯德尔的相关系数推导回归估计值，可以对斜率，截距和医疗决策点的偏差方差进行分析估计，而这些估计值目前尚不可用。此外，结果表明，使用Knight算法计算Kendall的tau可以在准线性时间内计算Passing–Bablok估计量。这样，即使对于非常大的数据集，也可以快速计算此估计量。还提供了来自临床医学数据的实例。