How to detect linear dependence on the copula level?

In many practical situations, the dependence between the quantities is linear or approximately linear. Knowing that the dependence is linear simplifies computations; so, is is desirable to detect linear dependencies. If we know the joint probability distribution, we can detect linear dependence by c...

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Main Authors:	Vladik Kreinovich, Hung T. Nguyen, Songsak Sriboonchitta
Format:	Book Series
Published:	2018
Subjects:	Computer Science Engineering
Online Access:	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84897890526&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/53436
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Institution:	Chiang Mai University

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spelling	th-cmuir.6653943832-534362018-09-04T09:51:55Z How to detect linear dependence on the copula level? Vladik Kreinovich Hung T. Nguyen Songsak Sriboonchitta Computer Science Engineering In many practical situations, the dependence between the quantities is linear or approximately linear. Knowing that the dependence is linear simplifies computations; so, is is desirable to detect linear dependencies. If we know the joint probability distribution, we can detect linear dependence by computing Pearson's correlation coefficient. In practice, we often have a copula instead of a full distribution; in this case, we face a problem of detecting linear dependence based on the copula. Also, distributions are often heavy-tailed, with infinite variances, in which case Pearson's formulas cannot be applied. In this paper, we show how to modify Pearson's formula so that it can be applied to copulas and to heavy-tailed distributions. © Springer International Publishing Switzerland 2014. 2018-09-04T09:49:10Z 2018-09-04T09:49:10Z 2014-01-01 Book Series 21945357 2-s2.0-84897890526 10.1007/978-3-319-03395-2_4 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84897890526&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/53436
institution	Chiang Mai University
building	Chiang Mai University Library
country	Thailand
collection	CMU Intellectual Repository
topic	Computer Science Engineering
spellingShingle	Computer Science Engineering Vladik Kreinovich Hung T. Nguyen Songsak Sriboonchitta How to detect linear dependence on the copula level?
description	In many practical situations, the dependence between the quantities is linear or approximately linear. Knowing that the dependence is linear simplifies computations; so, is is desirable to detect linear dependencies. If we know the joint probability distribution, we can detect linear dependence by computing Pearson's correlation coefficient. In practice, we often have a copula instead of a full distribution; in this case, we face a problem of detecting linear dependence based on the copula. Also, distributions are often heavy-tailed, with infinite variances, in which case Pearson's formulas cannot be applied. In this paper, we show how to modify Pearson's formula so that it can be applied to copulas and to heavy-tailed distributions. © Springer International Publishing Switzerland 2014.
format	Book Series
author	Vladik Kreinovich Hung T. Nguyen Songsak Sriboonchitta
author_facet	Vladik Kreinovich Hung T. Nguyen Songsak Sriboonchitta
author_sort	Vladik Kreinovich
title	How to detect linear dependence on the copula level?
title_short	How to detect linear dependence on the copula level?
title_full	How to detect linear dependence on the copula level?
title_fullStr	How to detect linear dependence on the copula level?
title_full_unstemmed	How to detect linear dependence on the copula level?
title_sort	how to detect linear dependence on the copula level?
publishDate	2018
url	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84897890526&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/53436
_version_	1681424134858342400

How to detect linear dependence on the copula level?

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