On choosing between two nonlinear models estimated robustly. Some Monte Carlo evidence

The article considers the problem of choosing between two (possibly) nonlinear models that have been fitted to the same data using M-estimation methods. An asymptotically normally distributed test statistic that takes into account the fact that the models are fitted robustly is given. The new procedure is compared with other test statistics using a Monte Carlo study. We found that the presence of a competitive model either in the null or the alternative hipothesis affects the distributional properties of the tests, and that in the case that the data contains outlying observations the new procedure had a significantly higher power than the rest of the tests.