High finite-sample efficiency and robustness based on distance-constrained maximum likelihood .

RICARDO A. MARONNA; VICTOR J. YOHAI

COMPUTATIONAL STATISTICS AND DATA ANALYSIS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2015 vol. 83 p. 262 - 274

0167-9473

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 ô -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 isproposed for parametric models, which is based on a distance between parameters. Givena 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, simulations show that the proposed estimator attains a finite-sample efficiency close to one while improving the robustness of the initial estimator. The same approach also shows good results in the estimation of multivariate location and scatter.