Robust estimation with high finite-sample efficiency through distance-constrained maximum likelihood

RICARDO A. MARONNA; VÍCTOR J. YOHAI

Londres

Conferencia; 6 th lnternational Conference of the ERCIM WG on Computational and Methodological Statistics (ERCIM 201 3; 2013

Good robust estimators can be tuned to combine a high breakdown point and a specified asymptotic efficiency at a central model. This happens in regression with MM- and tau-estimators among others. However, the finite sample efficiency of these estimators can be much lower than the asymptotic one. To overcome this drawback, an approach is proposed for parametric models. It is based on the distance between parameters induced by the Kullback-Leibler divergence. Given a robust estimator, the proposed one is obtained by maximizing the likelihood under the constraint that the distance is less than a given threshold. For the linear model with normal errors and using the MM estimator, simulations show that the proposed estimator attains a finite-sample efficiency close to one, while its maximum mean squared error is smaller than that of the MM estimator