to simulations, approximately 600 sample pairs are sufficient to determine an accurate confidence interval. Variations A variation of the Theil–Sen estimator, the repeated median regression of , determines for each sample point , the median of the slopes of lines through that point, and then determines the overall estimator as the median of these medians. It can tolerate a greater number of outliers than the Theil–Sen estimator, but known algorithms for computing it efficiently are more complicated and less practical. A different variant pairs up sample points by the rank of their -coordinates: the point with the smallest coordinate is paired with the first point above the median coordinate, the second-smallest point is paired with the next point above the median, and so on. It then computes the median of the slopes of the lines determined by these pairs of points, gaining speed by examining significantly fewer pairs than the Theil–Sen estimator. Variations of the Theil–Sen estimator based on weighted medians have also been studied, based on the principle that pairs of samples whose -coordinates differ more greatly are more likely to have an accurate slope and therefore should receive a higher weight. For seasonal data, it may be appropriate to smooth out seasonal variations in the data by considering only pairs of sample points that both belong to the same month or the same season of the year, and finding the median of the slopes of the lines determined by this more restrictive set of pairs. Statistical properties The Theil–Sen estimator is an unbiased estimator of the true slope in simple linear regression. For many distributions of the response error, this estimator has high asymptotic efficiency relative to least-squares estimation. Estimators with low efficiency require more independent observations to attain the same sample variance of efficient unbiased estimators. The Theil–Sen estimator is more robust than the least-squares estimator because it is much less sensitive to outliers. It has a breakdown point of meaning that it can tolerate arbitrary corruption of up to 29.3% of the input data-points without degradation of its accuracy. However, the breakdown point decreases for higher-dimensional generalizations of the method. A higher breakdown point, 50%, holds for a different robust line-fitting algorithm, the repeated median estimator of Siegel. The Theil–Sen estimator is equivariant under every linear transformation of its response variable, meaning that transforming the data first and then fitting a line, or fitting a line