Robust estimation in high dimensional Poisson regression models.

CLAUDIO AGOSTINELLI; MARINA VALDORA; VÍCTOR YOHAI

Workshop; Big and Complex Data Theory, Applications and Value Creation; 2018

Generalized Linear Models are routinely used in data analysis. Classical estimatorsare based on the maximum likelihood principle and it is well knownthat the presence of outliers can have a large impact on them. Several robustprocedures have been presented in the literature, being redescendingM-estimators the most widely accepted. Based on non-convex loss functions,these estimators need a robust initial estimate, which is often obtained bysubsampling techniques. However, as the number of unknown parametersincreases, the number of subsamples needed in order for this method to berobust, soon makes it infeasible. Furthermore the subsampling procedureprovides a non deterministic starting point. A new method for computinga robust initial estimator is proposed. This method is deterministic anddemands a relatively short computational time, even for large numbers ofcovariates. The proposed method is applied to M-estimators based on transformations.In addition, an iteratively reweighted least squares algorithm isproposed for the computation of the nal estimates. The new methods arestudied by means of Monte Carlo experiments.