2013/11/20 by Ricardo A. Maronna, Maronna, Ricardo, Vı́ctor J. Yohai +1
Decision Sciences · Mathematics · #62F35 #62J05 #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1311.5187
openalex publication_date 2013/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Good robust estimators can be tuned to combine a high breakdown point and a\nspecified asymptotic efficiency at a central model. This happens in regression\nwith MM- and tau-estimators among others. However, the finite-sample efficiency\nof these estimators can be much lower than the asymptotic one. To overcome this\ndrawback, an approach is proposed for parametric models, which is based on a\ndistance between parameters. Given a robust estimator, the proposed one is\nobtained by maximizing the likelihood under the constraint that the distance is\nless than a given threshold. For the linear model with normal errors and using\nthe MM estimator and the distance induced by the Kullback-Leibler divergence,\nsimulations show that the proposed estimator attains a finite-sample efficiency\nclose to one, while its maximum mean squared error under pointwise outlier\ncontamination is smaller than that of the MM estimator. The same approach also\nshows good results in the estimation of multivariate location and scatter.\n