Publication at Faculty of Mathematics and Physics |
2008
Abstract
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 derive stability results without precise knowledge of problem structure and without measurability assumption. The setup is illustrated on consistency of a $\varepsilon $-$M$-estimator in linear regression model.