Article révisé par les pairs
| Résumé : | Given a finite sequence of events and a well-defined notion of events beinginteresting, the Odds-theorem (Bruss(2000)) gives an online strategy to stop onthe last interesting event. This strategy is optimal for independent events, and itis obtained in a straightforward way by an algorithm which is optimal itself (oddsalgorithm).Here we study questions in how far the optimal value mirrors monotonicityproperties of the underlying sequence of probabilities of events. We make thesequestions precise, motivate them, and then give complete answers. The motivation isenhanced by certain problems where it seems desirable to apply the odds-algorithmbut where a lack of information does not allow to do so without incorporating sequentialestimation. In view of this goal, the notion of a plug-in odds-algorithm isintroduced. Several applications are included. |
