A rank estimator in robust regression is a minimizer of a function which depends (in addition to other factors) on the ordering of residuals but not on their values. Here we focus on the optimization aspects of rank estimators. We distinguish two classes of functions: a class with a continuous and convex objective function (CCC), which covers the class of rank estimators known from statistics, and also another class (GEN), which is far more general. We propose efficient algorithms for both classes. For GEN we propose an enumerative algorithm that works in polynomial time as long as the number of regressors is $O\left(1\right)$. The proposed algorithm utilizes the special structure of arrangements of hyperplanes that occur in our problem and is superior to other known algorithms in this area. For the continuous and convex case, we propose an unconditionally polynomial algorithm finding the exact minimizer, unlike the heuristic or approximate methods implemented in statistical packages.

稳健回归中的秩估计量是函数的最小化器，它取决于（除了其他因素之外）残差的顺序，但不取决于它们的值。在这里，我们关注排名估计器的优化方面。我们区分了两类函数：一类具有连续和凸目标函数 (CCC)，它涵盖了从统计学中已知的等级估计器类，以及另一类 (GEN)，它更通用。我们为这两个类别提出了有效的算法。对于 GEN，我们提出了一种枚举算法，只要回归器的数量为$○\left(1\right)$. 所提出的算法利用了我们问题中出现的超平面排列的特殊结构，并且优于该领域的其他已知算法。对于连续和凸的情况，我们提出了一种无条件多项式算法来找到精确的最小值，这与统计包中实现的启发式或近似方法不同。