Two choice optimal stopping
| dc.creator | Assaf, David | |
| dc.creator | Goldstein, Larry | |
| dc.creator | Samuel-Cahn, Ester | |
| dc.date | 2005-10-12 | |
| dc.date.accessioned | 2026-07-07T08:07:19Z | |
| dc.date.available | 2026-07-07T08:07:19Z | |
| dc.description | Let $X_n,...,X_1$ be i.i.d. random variables with distribution function $F$. A statistician, knowing $F$, observes the $X$ values sequentially and is given two chances to choose $X$'s using stopping rules. The statistician's goal is to stop at a value of $X$ as small as possible. Let $V_n^2$ equal the expectation of the smaller of the two values chosen by the statistician when proceeding optimally. We obtain the asymptotic behavior of the sequence $V_n^2$ for a large class of $F$'s belonging to the domain of attraction (for the minimum) ${\cal D}(G^α)$, where $G^α(x)=[1-\exp(-x^α)]{\bf I}(x \ge 0)$. The results are compared with those for the asymptotic behavior of the classical one choice value sequence $V_n^1$, as well as with the ``prophet value" sequence $V_n^p=E(\min\{X_n,...,X_1\})$. | |
| dc.description | 33 pages | |
| dc.identifier | https://arxiv.org/abs/math/0510242 | |
| dc.identifier | http://arxiv.org/abs/math/0510242 | |
| dc.identifier | Advances in Applied Probability 2004, Vol 36, 1116-1147 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130904 | |
| dc.subject | Probability | |
| dc.subject | Statistics Theory | |
| dc.subject | 60G40 | |
| dc.title | Two choice optimal stopping | |
| dc.type | text |