Redescending M-estimators and Deterministic Annealing, with Applications to Robust Regression and Tail Index Estimation

摘要

A new type of redescending M-estimators is constructed, based on dataaugmentation with an unspecified outlier model. Necessary and sufficientconditions for the convergence of the resulting estimators to the Hubertypeskipped mean are derived. By introducing a temperature parameter the concept ofdeterministic annealing can be applied, making the estimator insensitive to thestarting point of the iteration. The properties of the annealing M-estimator asa function of the temperature are explored. Finally, two applications arepresented. The first one is the robust estimation of interaction vertices inexperimental particle physics, including outlier detection. The second one isthe estimation of the tail index of a distribution from a sample using robustregression diagnostics.