Modern use of slope estimation often involves the (repeated) estimation of a large number of slopes on a large number of data points. Some of the most popular non-parametric and robust alternatives to the least squares estimator are the Theil-Sen and Siegel's repeated median slope estimators. The [robslopes](https://CRAN.R-project.org/package=robslopes) package contains fast algorithms for these slope estimators. The implemented randomized algorithms run in O(nlog(n)) and O(nlog²(n)) expected time respectively and use O(n) space. They achieve speedups up to a factor 10³ compared with existing implementations for common sample sizes, as illustrated in a benchmark study, and they allow for the possibility of estimating the slopes on samples of size 10⁵ and larger thanks to the limited space usage. Finally, the original algorithms are adjusted in order to properly handle duplicate values in the data set.
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Raymaekers et al. (2023) studied this question.
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