Theil-Sen

A reader recently inquired about using the Theil-Sen slope to estimate trends in temperature data, rather than the more usual least-squares regression. The Theil-Sen estimator is a non-parametric method to estimate a slope (perhaps more properly, a “distribution-free” method) which is robust, i.e., it is resistant to the presence of outliers (extremely variant data values) which can wreak havoc with least-squares regression. It also doesn’t rely on the noise following the normal distribution, it’s truly a distribution-free method. Even when the data are normally distributed and outliers are absent, it’s still competitive with least-squares regression.