GROS: A General Robust Aggregation Strategy

A new, very general, robust procedure for combining estimators in metric spaces is introduced (GROS).The method is reminiscent of the well-known median of means, as described in Devroye, Lerasle, Lugosi and Oliveira (2016).Initially, the sample is divided into K groups.Subsequently, an estimator is computed for each group.Finally, these K estimators are combined using a robust procedure.We prove that this estimator is sub-Gaussian and we get its breakdown point, in the sense of Donoho.The robust procedure involves a minimization problem on a general metric space, but we show that the same (up to a constant) sub-Gaussianity is obtained if the mini-1 Statistica Sinica: Newly accepted Paper mization is taken over the sample, making GROS feasible in practice.The performance of GROS is evaluated through five simulation studies: the first one focuses on classification using k-means, the second one on the multi-armed bandit problem, the third one on the regression problem.The fourth one is the set estimation problem under a noisy model.We apply GROS to get a robust persistent diagram.Lastly, an application of robust estimation techniques to determine the home-range of Canis dingo in Australia is implemented.