The Theil-Sen estimator, also called Sen's slope estimator or the Kendall-Theil robust line, is a method of robust estimation and nonparametric estimation for the slope
in simple linear regression. The estimator was
introduced by Theil (1950) and extended by Sen (1968). For data points 
, its slope estimate is the statistical
median of all pairwise slopes with distinct abscissas,
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An intercept can then be estimated by
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Because it uses a statistical median of slopes rather than a mean of squared residuals, the estimator is less sensitive to outliers than least squares fitting. Sen's formulation is associated with Kendall's tau: the slope can be obtained by inverting a Kendall rank-correlation test between the predictor and the fitted residuals (Sen 1968).
