Select sets: Rank and file
Abstract
In many situations, the decision maker observes items in sequence and needs to determine whether or not to retain a particular item immediately after it is observed. Any decision rule creates a set of items that are selected. We consider situations where the available information is the rank of a present observation relative to its predecessors. Certain ``natural'' selection rules are investigated. Theoretical results are presented pertaining to the evolution of the number of items selected, measures of their quality and the time it would take to amass a group of a given size.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- March 2007
- DOI:
- 10.48550/arXiv.math/0703032
- arXiv:
- arXiv:math/0703032
- Bibcode:
- 2007math......3032K
- Keywords:
-
- Mathematics - Probability;
- 62G99 (Primary) 62F07;
- 60F15 (Secondary)
- E-Print:
- Published at http://dx.doi.org/10.1214/105051606000000691 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)