Fast Algorithm for Computing the Upper Endpoint of Sample Variance for Interval Data: Case of Sufficiently Accurate Measurements

Fast Algorithm for Computing the Upper Endpoint of Sample Variance for Interval Data: Case of... When we have n results x 1,...,x n of repeated measurement of the same quantity, the traditional statistical approach usually starts with computing their sample average E and their sample variance V. Often, due to the inevitable measurement uncertainty, we do not know the exact values of the quantities, we only know the intervals x i of possible values of x 1 In such situations, for different possible values x i∈ x i, we get different values of the variance. We must therefore find the range V of possible values of V. It is known that in general, this problem is NP-hard. For the case when the measurements are sufficiently accurate (in some precise sense), it is known that we can compute the interval V in quadratic time O(n2). In this paper, we describe a new algorithm for computing V that requires time O(n log(n)) (which is much faster than O(n 2)). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Fast Algorithm for Computing the Upper Endpoint of Sample Variance for Interval Data: Case of Sufficiently Accurate Measurements

Loading next page...
 
/lp/springer_journal/fast-algorithm-for-computing-the-upper-endpoint-of-sample-variance-for-i3p1Kem0XQ
Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2006 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/s11155-006-2965-8
Publisher site
See Article on Publisher Site

Abstract

When we have n results x 1,...,x n of repeated measurement of the same quantity, the traditional statistical approach usually starts with computing their sample average E and their sample variance V. Often, due to the inevitable measurement uncertainty, we do not know the exact values of the quantities, we only know the intervals x i of possible values of x 1 In such situations, for different possible values x i∈ x i, we get different values of the variance. We must therefore find the range V of possible values of V. It is known that in general, this problem is NP-hard. For the case when the measurements are sufficiently accurate (in some precise sense), it is known that we can compute the interval V in quadratic time O(n2). In this paper, we describe a new algorithm for computing V that requires time O(n log(n)) (which is much faster than O(n 2)).

Journal

Reliable ComputingSpringer Journals

Published: Jan 1, 2006

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve Freelancer

DeepDyve Pro

Price
FREE
$49/month

$360/year
Save searches from
Google Scholar,
PubMed
Create lists to
organize your research
Export lists, citations
Read DeepDyve articles
Abstract access only
Unlimited access to over
18 million full-text articles
Print
20 pages/month
PDF Discount
20% off