Statistics Papers

Document Type

Journal Article

Date of this Version

2016

Publication Source

Mathematica Applicanda

Volume

44

Issue

1

Start Page

3

Last Page

16

DOI

10.14708/ma.v44i1.817

Abstract

The Bruss-Robertson inequality gives a bound on themaximal number of elements of a random sample whose sum is less than a specifiedvalue, and the extension of that inequality which is given hereneither requires the independence of the summands nor requires the equality of their marginal distributions. A review is also given of the applications of the Bruss-Robertson inequality,especially the applications to problems of combinatorial optimization such as the sequential knapsack problem and the sequential monotone subsequence selection problem.

Copyright/Permission Statement

This work is licensed under a Creative Commons Attribution 3.0 License.

Keywords

Order statistical inequalities, sequential knapsack problem, sequential monotone subsequence problem, sequential selection, online selection, Markov decision problems, resource dependent branching processes, Bellman equation

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Date Posted: 27 November 2017

This document has been peer reviewed.