A ROBUST TEST FOR NONNESTED HYPOTHESES

We propose a robust version of Cox-type test statistics for the choice between two nonnested hypotheses. We first show that the influence of small amounts of contamination in the data on the test decision can b e very large. Secondly, we build a robust test statistic by using the results on robust parametric tests that are available in the literatur e and show that the level of the robust test is stable. Finally, we sh ow numerically not only the robustness of this new test statistic but also that its asymptotic distribution is a good approximation of its s ample distribution, unlike for the classical test statistic. We apply our results to the choice between a Pareto and an exponential distribu tion as well as between two competing regressors in the simple linear regression model without intercept.