High Dimensional Robust M-Estimation: Asymptotic Variance via Approximate Message Passing

  title={High Dimensional Robust M-Estimation: Asymptotic Variance via Approximate Message Passing},
  author={David L. Donoho and Andrea Montanari},
In a recent article (Proc. Natl. Acad. Sci., 110(36), 14557-14562), El Karoui et al. study the distribution of robust regression estimators in the regime in which the number of parameters p is of the same order as the number of samples n. Using numerical simulations and ‘highly plausible’ heuristic arguments, they unveil a striking new phenomenon. Namely, the regression coefficients contain an extra Gaussian noise component that is not explained by classical concepts such as the Fisher… CONTINUE READING
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