# Exact Bounds on Finite Populations of Interval Data

Ontology type: schema:ScholarlyArticle      Open Access: True

### Article Info

DATE

2005-06

AUTHORS ABSTRACT

In this paper, we start research into using intervals to bound the impact of bounded measurement errors on the computation of bounds on finite population parameters (“descriptive statistics”). Specifically, we provide a feasible (quadratic time) algorithm for computing the lower bound \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\underline{\sigma^2}$$\end{document} on the finite population variance function of interval data. We prove that the problem of computing the upper bound \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{\sigma}^2$$\end{document} is, in general, NP-hard. We provide a feasible algorithm that computes \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{\sigma}^2$$\end{document} under reasonable easily verifiable conditions, and provide preliminary results on computing other functions of finite populations. More... »

PAGES

207-233

### Journal

TITLE

Reliable Computing

ISSUE

3

VOLUME

11

### Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11155-005-3616-1

DOI

http://dx.doi.org/10.1007/s11155-005-3616-1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1034825891

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