Empirical Estimates in Stochastic Optimization: Special cases

0359099 - ÚTIA 2012 RIV CZ eng K - Conference Paper (Czech conference)
Kaňková, Vlasta
Empirical Estimates in Stochastic Optimization: Special cases.
Výpočtová ekonomie, sborník 4.semináře. Plzeň: Západočeská univerzita v Plzni, 2010 - (Lukáš, L.), s. 9-19. ISBN 978-80-7043-773-5.
[Výpočtová ekonomie, 4. seminář. Plzeň (CZ), 18.12.2008]
R&D Projects: GA ČR GAP402/10/0956; GA ČR GA402/07/1113; GA ČR(CZ) GA402/08/0107; GA ČR(CZ) GA402/06/0990
Institutional research plan: CEZ:AV0Z10750506
Keywords : stochastic programming problems * L_1 norm * Lipschitz property * empirical estimates * convergence rate * exponential tails * heavy tails * Pareto distribution * risk functional
Subject RIV: BB - Applied Statistics, Operational Research
http://library.utia.cas.cz/separaty/2011/E/kankova-empirical estimates in stochastic optimization special cases.pdf

Classical optimization problems depending on a probability measure belong mostly to nonlinear deterministic optimization problems that are relatively complicated. On the other hand, these problems fulfil very often "suitable" mathematical properties guaranteing the stability (w.r.t. probability measure) and, moreover, giving a possibility to replace the "underlying" probability measure by an empirical one to obtain "good" stochastic estimates of the optimal value and the optimal solution. Properties of thess estimates have been investigated mostly for standard types of probability measures with suitable (thin) tails and independent random samples. However distributions with heavy tails correspond to many economic problems and, moreover, many applications do not correspond to the "classical" problems. The aim of the paper is, first, to try to recall stability results including also heavy tails and more general problems.
Permanent Link: http://hdl.handle.net/11104/0196952