If the distribution of the random parameters of a stochastic program is unknown, the empirical distribution based on a sample may be used as a proxy. This empirical approximation is related to the “true” stochastic program in the same way as a statistical estimate is related to the true parameter value. Properties of statistical estimators, like consistency, asymptotical distributions and the construction of confidence regions are reviewed in the realm of stochastic optimization. The entropic size of a stochastic program determines the quality of the approximation. In case that random constraints are present, the notion of epiconvergence replaces in a natural way the notion of uniform convergence of functions. The asymptotic structures are described by the asymptotic stochastic program associated to the sequence of empirical programs.
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