# Exact Bounds on Finite Populations of Interval Data

Exact Bounds on Finite Populations of Interval Data 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 $$\underline{\sigma^2}$$ on the finite population variance function of interval data. We prove that the problem of computing the upper bound $$\bar{\sigma}^2$$ is, in general, NP-hard. We provide a feasible algorithm that computes $$\bar{\sigma}^2$$ under reasonable easily verifiable conditions, and provide preliminary results on computing other functions of finite populations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# Exact Bounds on Finite Populations of Interval Data

, Volume 11 (3) – Jan 1, 2005
27 pages

/lp/springer_journal/exact-bounds-on-finite-populations-of-interval-data-axXGln0vNG
Publisher
Springer Journals
Copyright © 2005 by Springer Science + Business Media, Inc.
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1007/s11155-005-3616-1
Publisher site
See Article on Publisher Site

### 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 $$\underline{\sigma^2}$$ on the finite population variance function of interval data. We prove that the problem of computing the upper bound $$\bar{\sigma}^2$$ is, in general, NP-hard. We provide a feasible algorithm that computes $$\bar{\sigma}^2$$ under reasonable easily verifiable conditions, and provide preliminary results on computing other functions of finite populations.

### Journal

Reliable ComputingSpringer Journals

Published: Jan 1, 2005

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