par Dendievel, Rémi 
Référence Statistics & probability letters, 97, page (176-184)
Publication Publié, 2015-02
Référence Statistics & probability letters, 97, page (176-184)
Publication Publié, 2015-02
Article révisé par les pairs
| Résumé : | One way to interpret the classical secretary problem (CSP) is to consider it as a special case of the following problem. We observe n independent indicator variables I1, I2, ..., In sequentially and we try to stop on the last variable being equal to 1. If Ik=1 it means that the kth observed secretary has smaller rank than all previous ones (and therefore is a better secretary). In the CSP, pk=E(Ik)=1/k and the last k with Ik=1 stands for the best candidate. The more general problem of stopping on a last "1" was studied by Bruss (2000). In what we will call Weber's problem the indicators are replaced by random variables which can take more than 2 values. The goal is now to maximize the probability of stopping on a value appearing for the last time in the sequence. Notice that we do not fix in advance the value taken by the variable on which we stop. We can solve this problem in some cases and provide efficient algorithms to compute the optimal stopping rules. These cases carry generality and are applicable in many concrete situations. |
