A new robust estimation approach: An extended threshold M-estimator procedure

In order to tackle more efficiently the parameters estimation of an Output Error (OE) models contaminated by outliers, we propose to extend the range of the scaling factor of a parameterized robust estimation criterion (PREC) in the Huber's M-estimates context based on a mixed norm. Moreover, since the gradient and the Hessian of the PREC present a nonlinear structure in the OE models, we propose a new method to establish an L-Finite Taylor's Expansion of these expressions in order to provide the asymptotic covariance matrix of the robust estimator. We present the results of a Monte Carlo study and we compare some robust methods with respect to our procedure.