Finite Sample Size Results for Robust

The problem of model selection in the face of nite sample size is considered within the framework of statistical decision theory. Focusing on the special case of regression, we introduce a model selection criterion which is shown to be robust in the sense that, with high conndence, even for a nite sample size it selects the best model. Our derivation is based on uniform convergence methods , augmented by results from the theory of function approximation, which permit us to make deenite probabilistic statements about the nite sample behavior. These results stand in contrast to classical approaches, which can only guarantee the asymptotic optimality of the choice. The criterion is demonstrated for the problem of model selection in feedforward neural networks. Index Terms|Statistical model selection, uniform strong law of large numbers , structural risk minimization, lower and upper bounds on approximation error, algorithmic complexity, neural networks.