| Title:
|
Stability of stochastic optimization problems - nonmeasurable case (English) |
| Author:
|
Lachout, Petr |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
44 |
| Issue:
|
2 |
| Year:
|
2008 |
| Pages:
|
259-276 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
stability of stochastic optimization problem |
| Keyword:
|
weak convergence of probability measures |
| Keyword:
|
estimator consistency |
| Keyword:
|
metric spaces |
| MSC:
|
60B05 |
| MSC:
|
62F10 |
| MSC:
|
62J05 |
| MSC:
|
90C15 |
| MSC:
|
90C31 |
| idZBL:
|
Zbl 1154.90559 |
| idMR:
|
MR2428223 |
| . |
| Date available:
|
2009-09-24T20:33:58Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135847 |
| . |
| Reference:
|
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| . |
