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- Title
THE SECRETARY PROBLEM OF MINIMIZING THE EXPECTED RANK: A SIMPLE SUBOPTIMAL APPROACH WITH GENERALIZATIONS.
- Authors
Krieger, Abba M.; Samuel-Cahn, Ester
- Abstract
The secretary problem for selecting one item so as to minimize its expected rank, based on observing the relative ranks only, is revisited. A simple suboptimal rule, which performs almost as well as the optimal rule, is given. The rule stops with the smallest i such that Ri ≤ ic/(n+1-i) for a given constant c, where Ri is the relative rank of the ith observation and n is the total number of items. This rule has added flexibility. A curtailed version thereof can be used to select an item with a given probability P, P<1. The rule can be used to select two or more items. The problem of selecting a fixed percentage, α, 0<α<1, of n, is also treated. Numerical results are included to illustrate the findings.
- Subjects
PROBABILITY theory; MATHEMATICAL statistics; NUMERICAL analysis; ASYMPTOTIC expansions; DIFFERENCE equations
- Publication
Advances in Applied Probability, 2009, Vol 41, Issue 4, p1041
- ISSN
0001-8678
- Publication type
Article
- DOI
10.1239/aap/1261669585