Robust regression using repeated medians

Abstract

The repeated median algorithm is a robustified U -statistic in which nested medians replace the single mean. Unlike many generalizations of the univariate median, repeated median estimates maintain the high 50% breakdown value and can resist the effects of outliers even when they comprise nearly half of the data. For bivariate linear regression with symmetric errors, repeated median estimates are unbiased and Fisher consistent, and their efficiency under Gaussian sampling can be comparable to the efficiency of the univariate median.