Robslopes: Efficient Computation of the (Repeated) Median Slope

Abstract

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 $\mathcal{O}(n\log(n))$ and $\mathcal{O}(n\log^2(n))$ expected time respectively and use $\mathcal{O}(n)$ space. They achieve speedups up to a factor $10^3$ 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 $10^5$ 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.