Theil–Sen estimator
In non-parametric statistics, there is a method for robustly fitting a line to a set of points (simple linear regression) that chooses the median of the slopes of all lines through pairs of two-dimensional sample points. It has been called the Theil–Sen estimator, Sen's slope estimator,slope selection, the single median method, the Kendall robust line-fit method, and the Kendall–Theil robust line. It is named after Henri Theil and Pranab K. Sen, who published papers on this method in 1950 and 1968 respectively, and after Maurice Kendall.
This estimator can be computed efficiently, and is insensitive to outliers. It can be significantly more accurate than non-robust simple linear regression for skewed and heteroskedastic data, and competes well against non-robust least squares even for normally distributed data in terms of statistical power. It has been called "the most popular nonparametric technique for estimating a linear trend".
As defined by Theil (1950), the Theil–Sen estimator of a set of two-dimensional points (xi,yi) is the median m of the slopes (yj − yi)/(xj − xi) determined by all pairs of sample points. Sen (1968) extended this definition to handle the case in which two data points have the same x-coordinate. In Sen's definition, one takes the median of the slopes defined only from pairs of points having distinct x-coordinates.
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