Empirical Estimates in Stochastic Optimization via Distribution Tails

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 MŠMT(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.
Permanent Link: http://hdl.handle.net/11104/0187260