Data-driven model choice in multivariate nonparametric regression

The problem of choosing between different regression models, is investigated. A completely automatic model selection procedure is defined and asymptotic optimality results are shown. These results are stated in a general framework including as well nested as unnested situations, including as well i.i.d. as dependent samples, and without specifying any class of non-parametric smoothers. Because of the well-known curse of dimensionality, model selection is of particular interest in multivariate regression settings, and it will be discussed how the previous general model choice approach can be used in several different highdimensional situations.