In this paper we propose a sufficient dimension reduction algorithm based on the difference of inverse medians. The classic methodology based on inverse means in each slice was recently extended, by using inverse medians, to robustify existing methodology at the presence of outliers. Our effort is focused on using differences between inverse medians in pairs of slices. We demonstrate that our method outperforms existing methods at the presence of outliers. We also propose a second algorithm which is not affected by the ordering of slices when the response variable is categorical with no underlying ordering of its values.

中文翻译：

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切片逆中位数差回归

在本文中，我们提出了一种基于反中位数差异的充分降维算法。最近，通过使用反中位数，对每个切片中基于逆均值的经典方法进行了扩展，以在存在异常值时增强现有方法的可靠性。我们的工作重点是利用成对的切片中的反向中位数之间的差异。我们证明，在存在异常值的情况下，我们的方法优于现有方法。我们还提出了第二种算法，当响应变量是分类的且其值没有基础排序时，该算法不受条带排序的影响。