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B0390
Title: Robust and efficient regression Authors:  Guy Nason - Imperial College, London (United Kingdom) [presenting]
Abstract: It is known that L1/median/quantile based regressions perform better than L2/mean-based regressions in the presence of outliers, but that the latter is more statistically efficient for light tailed data. We develop a new method that is almost as efficient as L2 methods on light tailed data and almost as robust as L1 methods in the presence of outliers and adapts automatically to the different regimes. The new method relies on a new multiscale measure of location which is fast to compute and has an interesting non-multiscale interpretation in terms of standard statistics. We exhibit the new estimator on a range of regression problems.