Automatic Forward Search

This article was stimulated by the work of Atkinson and Riani (2000) on the estimation of regression models using a robust methodology called by the authors “forward search”, which seems to work well in the estimation of a variety of models, particularly when part of the data are generated by models different from the one we intend to estimate. The methodology detects the presumed outliers and allows the estimation of the model without them. The weak (perhaps strong) point of the procedure is, in our opinion, the fact that the choice of the final set of data to be used for the estimation is left to the researcher who relies on the behavior, often the visual behavior, of some statistics, as observations are added to an initial small subset of the data at hand. The choice is hence subjective and by its very nature impedes the use of simulations to judge how good the method is. The paper proposes some automatic ways of making this choice which allows the running of simulations in order to assess the properties of the estimators and make comparisons with alternative ways of estimating the models involved. We ran some simulations with the proposed methodology, computed efficiency of the estimators and compared it with OLS and LMS estimators.