Abstract
Abstract In a bivariate (x, y) scatterplot the three-group resistant line is that line for which the median residual in each outer third of the data (ordered on x) is zero. It was proposed by Tukey as an exploratory method resistant to outliers in x and y and suited to hand calculation. A dual plot representation of the procedure yields a fast, convergent algorithm, nonparametric confidence intervals for the slope, consistency, influence function, and asymptotic normality results. Monte Carlo results show that small sample efficiencies exceed their asymptotic values in important cases. Both breakdown and efficiency are adequate for exploratory work. Replacing medians by other M-estimators of location increases efficiency substantially without affecting breakdown or computational complexity. The method thus combines bounded influence and acceptable efficiency with conceptual and computational simplicity.
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