Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/44205
Title: Tight bounds on expected order statistics
Authors: Bertsimas, D.
Natarajan, K. 
Teo, C.-P. 
Issue Date: 2006
Source: Bertsimas, D.,Natarajan, K.,Teo, C.-P. (2006). Tight bounds on expected order statistics. Probability in the Engineering and Informational Sciences 20 (4) : 667-686. ScholarBank@NUS Repository.
Abstract: In this article, we study the problem of finding tight bounds on the expected value of the kth-order statistic E [Xk:n] under first and second moment information on n real-valued random variables. Given means E[Xi] = μi and variances Var [Xi] = σi 2, we show that the tight upper bound on the expected value of the highest-order statistic E[Xn:n] can be computed with a bisection search algorithm. An extremal discrete distribution is identified that attains the bound, and two closed-form bounds are proposed. Under additional covariance information Cov[Xi, Xj] = Qij, we show that the tight upper bound on the expected value of the highest-order statistic can be computed with semidefinite optimization. We generalize these results to find bounds on the expected value of the kth-order statistic under mean and variance information. For k < n, this bound is shown to be tight under identical means and variances. All of our results are distribution-free with no explicit assumption of independence made. Particularly, using optimization methods, we develop tractable approaches to compute bounds on the expected value of order statistics. © 2006 Cambridge University Press.
Source Title: Probability in the Engineering and Informational Sciences
URI: http://scholarbank.nus.edu.sg/handle/10635/44205
ISSN: 02699648
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.

Page view(s)

67
checked on Jan 12, 2018

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.