Inference of statistical bounds for multistage stochastic programming problems

Alexander Shapiro

Mathematical Methods of Operations Research, 2003, vol. 58, issue 1, 57-68

Abstract: We discuss in this paper statistical inference of sample average approximations of multistage stochastic programming problems. We show that any random sampling scheme provides a valid statistical lower bound for the optimal (minimum) value of the true problem. However, in order for such lower bound to be consistent one needs to employ the conditional sampling procedure. We also indicate that fixing a feasible first-stage solution and then solving the sampling approximation of the corresponding (T−1)-stage problem, does not give a valid statistical upper bound for the optimal value of the true problem. Copyright Springer-Verlag 2003

Keywords: Stochastic programming; Multistage stochastic programs with recourse; Monte Carlo sampling; Statistical bounds; Consistent estimators (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/s001860300280

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