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Empirical Estimates in Stochastic Optimization via Distribution Tails
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SYSNO ASEP 0346165 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Empirical Estimates in Stochastic Optimization via Distribution Tails Author(s) Kaňková, Vlasta (UTIA-B) RID Source Title Kybernetika. - : Ústav teorie informace a automatizace AV ČR, v. v. i. - ISSN 0023-5954
Roč. 46, č. 3 (2010), s. 459-471Number of pages 13 s. Action International Conference on Mathematical Methods in Economy and Industry Event date 15.06.2009-18.06.2009 VEvent location České Budějovice Country CZ - Czech Republic Event type CST Language eng - English Country CZ - Czech Republic 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 R&D Projects GA402/07/1113 GA ČR - Czech Science Foundation (CSF) GA402/08/0107 GA ČR - Czech Science Foundation (CSF) LC06075 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) CEZ AV0Z10750506 - UTIA-B (2005-2011) UT WOS 000280425000011 Annotation 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. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2011
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