Model selection: Consistency and robustness properties of the Schwarz Information Criterion for generalized M-estimatio

This thesis main focus are the robustness properties of the Schwarz Information Criterion (SIC) based on sample objective functions defining (Bias) robust M-estimators. The Bayesian underpinnings of such a criterion are established by extending Schwarz's original framework to densities not belonging to the exponential family. A definition of qualitative robustness appropriate for model selection is provided and it is shown that the crucial restriction needed to achieve robustness is the uniform boundedness of the objective function defining Bias robust M-estimators. In this process, the asymptotic performance of the SIC for generalized M-estimators is also studied. The finite sample behavior of the SIC for different types of M-estimators is analyzed by means of Monte Carlo experiments.