Robust Model Selection and M-Estimation

This paper studies the qualitative robustness properties of the Schwarz information criterion (SIC) based on objective functions defining <italic>M</italic>-estimators. A definition of qualitative robustness appropriate for model selection is provided and it is shown that the crucial restriction needed to achieve robustness in model selection is the uniform boundedness of the objective function. In the process, the asymptotic performance of the SIC for general <italic>M</italic>-estimators is also studied. The paper concludes with a Monte Carlo study of the finite sample behavior of the SIC for different specifications of the sample objective function.