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Empirical Estimates in Stochastic Optimization via Distribution Tails

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    0346165 - ÚTIA 2011 RIV CZ eng J - Journal Article
    Kaňková, Vlasta
    Empirical Estimates in Stochastic Optimization via Distribution Tails.
    Kybernetika. Roč. 46, č. 3 (2010), s. 459-471. ISSN 0023-5954.
    [International Conference on Mathematical Methods in Economy and Industry. České Budějovice, 15.06.2009-18.06.2009]
    R&D Projects: GA ČR GA402/07/1113; GA ČR(CZ) GA402/08/0107; GA MŠk(CZ) LC06075
    Institutional research plan: CEZ:AV0Z10750506
    Keywords : Stochastic programming problems * Stability * Wasserstein metric * L_1 norm * Lipschitz property * Empirical estimates * Convergence rate * Exponential tails * Heavy tails * Pareto distribution * Risk functional * Empirical quantiles
    Subject RIV: BB - Applied Statistics, Operational Research
    Impact factor: 0.461, year: 2010

    Classical optimization problems depending on a probability measure belong mostly to nonlinear deterministic problems that are, from the numerical point of view, relatively complicated. On the other hand, these problems fulfil very often assumptions giving a possibility to replace the ``underlying" probability measure by an empirical one to obtain ``good" empirical estimates of the optimal value and the optimal solution. Convergence rate of these estimates have been studied mostly for ``underlying" probability measure with suitable (thin) tails. However it is known that probability distributions with heavy tails better correspond to many economic problems. The paper focus on distributions with finite first moments and heavy tails. The introduced assertions are based on the stability results corresponding to the Wasserstein metric with an ``underlying" l_1 norm and empirical quantiles convergence.
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