Statistical Inference of Stochastic Optimization Problems
We discuss in this paper statistical inference of Monte Carlo simulation based approximations of stochastic optimization problems, where the “true” objective function, and probably some of the constraints, are estimated, typically by averaging a random sample. The classical maximum likelihood estimation can be considered in that framework. Recently statistical analysis of such methods has been motivated by a development of simulation based optimization techniques. We investigate asymptotic properties of the optimal value and an optimal solution of the corresponding Monte Carlo simulation approximations by employing the so-called Delta method, and discuss some examples.
KeywordsStochastic Programming Random Element Order Expansion Unique Optimal Solution True Problem
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