Article contents
Optimal Sequential selection of n random variables under a constraint
Published online by Cambridge University Press: 14 July 2016
Abstract
We observe a sequence {Xk}k≧1 of i.i.d. non-negative random variables one at a time. After each observation, we select or reject the observed variable. A variable that is rejected may not be recalled. We want to select N variables as soon as possible subject to the constraint that the sum of the N selected variables does not exceed some prescribed value C > 0. In this paper, we develop a sequential selection procedure that minimizes the expected number of observed variables, and we study some of its properties. We also consider the situation where N → ∞and C/N → α > 0. Some applications are briefly discussed.
- Type
- Research Papers
- Information
- Copyright
- Copyright © Applied Probability Trust 1984
Footnotes
This author's research was done while consulting at Bell Laboratories.
References
- 5
- Cited by