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Abstract: We introduce a large family of model selection tests based on the expectation of an arbitrary, possibly non-smooth, parametric criterion function of the data. It covers the case of strictly locally non-nested models and some overlapping models. The asymptotic theory of the proposed test statistic will be presented. A general exchangeable bootstrap scheme allows the evaluation of its limiting law as well as its asymptotic variance. In a simulation study, we empirically verify the distributional approximation of our test statistic in a finite sample and examine the empirical level and power of the corresponding model selection tests in various settings. Finally, an analysis of a financial dataset illustrates the proposed model selection procedure at work. The talk is based on a joint work with Florian Brueck and Jean-David Fermanian.