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Stability of stochastic optimization problems - nonmeasurable case
Kybernetika, Tome 44 (2008) no. 2, pp. 259-276 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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This paper deals with stability of stochastic optimization problems in a general setting. Objective function is defined on a metric space and depends on a probability measure which is unknown, but, estimated from empirical observations. We try to derive stability results without precise knowledge of problem structure and without measurability assumption. Moreover, $\varepsilon $-optimal solutions are considered. The setup is illustrated on consistency of a $\varepsilon $-$M$-estimator in linear regression model.
This paper deals with stability of stochastic optimization problems in a general setting. Objective function is defined on a metric space and depends on a probability measure which is unknown, but, estimated from empirical observations. We try to derive stability results without precise knowledge of problem structure and without measurability assumption. Moreover, $\varepsilon $-optimal solutions are considered. The setup is illustrated on consistency of a $\varepsilon $-$M$-estimator in linear regression model.
Classification : 60B05, 62F10, 62J05, 90C15, 90C31
Keywords: stability of stochastic optimization problem; weak convergence of probability measures; estimator consistency; metric spaces 
@article{KYB_2008_44_2_a8,
     author = {Lachout, Petr},
     title = {Stability of stochastic optimization problems - nonmeasurable case},
     journal = {Kybernetika},
     pages = {259--276},
     year = {2008},
     volume = {44},
     number = {2},
     mrnumber = {2428223},
     zbl = {1154.90559},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2008_44_2_a8/}
}
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Lachout, Petr. Stability of stochastic optimization problems - nonmeasurable case. Kybernetika, Tome 44 (2008) no. 2, pp. 259-276. http://geodesic.mathdoc.fr/item/KYB_2008_44_2_a8/

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