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Vincent Guigues(vguiguesfgv.br) Abstract: We study statistical properties of the optimal value and optimal solutions of the Sample Average Approximation of risk averse stochastic problems. Central Limit Theorem type results are derived for the optimal value and optimal solutions when the stochastic program is expressed in terms of a law invariant coherent risk measure. The obtained results are applied to hypotheses testing problems aiming at comparing the optimal values of several risk averse convex stochastic programs on the basis of samples of the underlying random vectors. We also consider nonasymptotic tests based on confidence intervals on the optimal values of the stochastic programs obtained using the Stochastic Mirror Descent algorithm. Numerical simulations show how to use our developments to choose among different distributions and show the superiority of the asymptotic tests on a class of risk averse stochastic programs. Keywords: Stochastic optimization, statistical inference, hypotheses testing, coherent risk measure, Central Limit Theorem, Sample Average Approximation Category 1: Stochastic Programming Category 2: Applications  Science and Engineering (Statistics ) Citation: Download: [PDF] Entry Submitted: 03/23/2016 Modify/Update this entry  
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