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A measure of dependence between two compositions

Bergman, Jakob LU and Holmquist, Björn LU (2012) In Australian & New Zealand Journal of Statistics 54(4). p.451-461
Abstract
We consider the problem of describing the correlation between two compositions. Using a bicompositional Dirichlet distribution, we calculate a joint correlation coefficient, based on the concept of information gain, between two compositions. Numerical values of the joint correlation coefficient are calculated for compositions of two and three components. We also present an estimator of the joint correlation coefficient for a sample from a bicompositional Dirichlet distribution. Two confidence intervals are also presented and we examine their empirical confidence coefficient using Monte Carlo study. Finally we apply the estimator to a data set analysing the correlation between the 1967 and 1997, and the 1977 and 1997 compositions of the... (More)
We consider the problem of describing the correlation between two compositions. Using a bicompositional Dirichlet distribution, we calculate a joint correlation coefficient, based on the concept of information gain, between two compositions. Numerical values of the joint correlation coefficient are calculated for compositions of two and three components. We also present an estimator of the joint correlation coefficient for a sample from a bicompositional Dirichlet distribution. Two confidence intervals are also presented and we examine their empirical confidence coefficient using Monte Carlo study. Finally we apply the estimator to a data set analysing the correlation between the 1967 and 1997, and the 1977 and 1997 compositions of the government gross domestic product for the 50 U.S. states and District of Columbia. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
correlation, Dirichlet distribution, empirical confidence coefficient, Fraser information, joint correlation coefficient, simplex
in
Australian & New Zealand Journal of Statistics
volume
54
issue
4
pages
451 - 461
publisher
Wiley-Blackwell
external identifiers
  • wos:000313888400004
  • scopus:84872818420
ISSN
1467-842X
DOI
10.1111/j.1467-842X.2012.00688.x
language
English
LU publication?
yes
id
d48774fb-e9ce-4745-bb2d-ab127732a475 (old id 1971432)
alternative location
http://onlinelibrary.wiley.com/doi/10.1111/j.1467-842X.2012.00688.x/abstract
date added to LUP
2013-01-09 13:15:45
date last changed
2017-01-01 06:12:30
@article{d48774fb-e9ce-4745-bb2d-ab127732a475,
  abstract     = {We consider the problem of describing the correlation between two compositions. Using a bicompositional Dirichlet distribution, we calculate a joint correlation coefficient, based on the concept of information gain, between two compositions. Numerical values of the joint correlation coefficient are calculated for compositions of two and three components. We also present an estimator of the joint correlation coefficient for a sample from a bicompositional Dirichlet distribution. Two confidence intervals are also presented and we examine their empirical confidence coefficient using Monte Carlo study. Finally we apply the estimator to a data set analysing the correlation between the 1967 and 1997, and the 1977 and 1997 compositions of the government gross domestic product for the 50 U.S. states and District of Columbia.},
  author       = {Bergman, Jakob and Holmquist, Björn},
  issn         = {1467-842X},
  keyword      = {correlation,Dirichlet distribution,empirical confidence coefficient,Fraser information,joint correlation coefficient,simplex},
  language     = {eng},
  number       = {4},
  pages        = {451--461},
  publisher    = {Wiley-Blackwell},
  series       = {Australian & New Zealand Journal of Statistics},
  title        = {A measure of dependence between two compositions},
  url          = {http://dx.doi.org/10.1111/j.1467-842X.2012.00688.x},
  volume       = {54},
  year         = {2012},
}