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Empirical Estimates in Stochastic Optimization via Distribution Tails

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    SYSNO ASEP0346165
    Document TypeJ - Journal Article
    R&D Document TypeJournal Article
    Subsidiary JČlánek ve WOS
    TitleEmpirical Estimates in Stochastic Optimization via Distribution Tails
    Author(s) Kaňková, Vlasta (UTIA-B) RID
    Source TitleKybernetika. - : Ústav teorie informace a automatizace AV ČR, v. v. i. - ISSN 0023-5954
    Roč. 46, č. 3 (2010), s. 459-471
    Number of pages13 s.
    ActionInternational Conference on Mathematical Methods in Economy and Industry
    Event date15.06.2009-18.06.2009
    VEvent locationČeské Budějovice
    CountryCZ - Czech Republic
    Event typeCST
    Languageeng - English
    CountryCZ - Czech Republic
    KeywordsStochastic 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 RIVBB - Applied Statistics, Operational Research
    R&D ProjectsGA402/07/1113 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)
    CEZAV0Z10750506 - UTIA-B (2005-2011)
    UT WOS000280425000011
    AnnotationClassical 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.
    WorkplaceInstitute of Information Theory and Automation
    ContactMarkéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201.
    Year of Publishing2011
Number of the records: 1  

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