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Initial robust estimation in generalized linear models

Agostinelli, Claudio, Valdora, Marina, Yohai, Victor J.
Computational statistics & data analysis 2019 v.134 pp. 144-156
Monte Carlo method, algorithms, least squares, linear models, methodology
Generalized Linear Models are routinely used in data analysis. Classical estimators are based on the maximum likelihood principle and it is well known that the presence of outliers can have a large impact on them. Several robust procedures have been presented in the literature, being redescending M-estimators the most widely accepted. Based on non-convex loss functions, these estimators need a robust initial estimate, which is often obtained by subsampling techniques. However, as the number of unknown parameters increases, the number of subsamples needed in order for this method to be robust, soon makes it infeasible. Furthermore the subsampling procedure provides a non deterministic starting point. A new method for computing a robust initial estimator is proposed. This method is deterministic and demands a relatively short computational time, even for large numbers of covariates. The proposed method is applied to M-estimators based on transformations. In addition, an iteratively reweighted least squares algorithm is proposed for the computation of the final estimates. The new methods are studied by means of Monte Carlo experiments.