Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Dependence Modeling

Ed. by Puccetti, Giovanni

1 Issue per year



Emerging Science

Open Access
Online
ISSN
2300-2298
See all formats and pricing
More options …

Global correlation and uncertainty accounting

Roger M. Cooke / Sassan Saatchi / Stephen Hagen
Published Online: 2016-09-23 | DOI: https://doi.org/10.1515/demo-2016-0009

Abstract

For a high dimensional field of random variables, global correlation is defined as the ratio of average covariance and average variance, and its elementary properties are studied. Global correlation is used to harmonize uncertainty assessments at global and local scales. It can be estimated by the correlation of random aggregations of fixed size of disjoint sets of random variables. Illustrative applications are given using crop loss per county per year and forest carbon.

Keywords: global correlation; forest carbon; uncertainty accounting

References

  • [1] Bedford, T. and R. M. Cooke (2002). Vines – a new graphical model for dependent random variables. Ann. Statist. 30(4), 1031–1068. CrossrefGoogle Scholar

  • [2] Cooke, R. M. (1997). Markov and entropy properties of tree and vine-dependent variables. In Proceedings of the Section on Bayesian Statistical Science. American Statistical Association, Alexandria VA. Google Scholar

  • [3] Cooke, R. M., C. Kousky, and H. Joe (2011). Micro correlations and tail dependence. In Dependence modeling, pp. 89–112. World Sci. Publ., Hackensack, NJ. Google Scholar

  • [4] Hanea, A.M. and G.F. Nane, (2016). The Asymptotic Distribution of the Determinant of a Random CorrelationMatrix. Preprint available at http://arxiv.org/abs/1309.7268. Google Scholar

  • [5] Holmes, R. B. (1991). On random correlation matrices. SIAM J. Matrix Anal. Appl. 12(2), 239–272. CrossrefGoogle Scholar

  • [6] Hotelling, H. (1936). Relations between two sets of variates. Biometrika 28(3/4), 321–377. CrossrefGoogle Scholar

  • [7] Houghton, R. A., F. Hall, and S. J. Goetz (2009). Importance of biomass in the global carbon cycle. J. Geophys. Res. Biogeosci. 114(G2). Google Scholar

  • [8] Joe, H. (2006). Generating random correlation matrices based on partial correlations. J. Multivariate Anal. 97(10), 2177– 2189. CrossrefGoogle Scholar

  • [9] Kendall, M. G. and A. Stuart (1967). The Advanced Theory of Statistics. Vol. 2: Inference and Relationship. Second edition. Hafner Publishing Co., New York. Google Scholar

  • [10] Koch, G. G. (2006). Intraclass correlation coefficient. In Encyclopedia of Statistical Sciences 6. JohnWiley & Sons, New York. Google Scholar

  • [11] Kousky, C. and R. M. Cooke (2011). The limits of securitization: micro-correlations, fat tails and tail dependence. In K. Boecker (Ed.), Re-Thinking Risk Measurement and Reporting, Uncertainty, Bayesian Analysis and Expert Judgement, pp. 295–330. Risk Books, London. Google Scholar

  • [12] Lewandowski, D., D. Kurowicka, and H. Joe (2009). Generating random correlation matrices based on vines and extended onion method. J. Multivariate Anal. 100(9), 1989–2001. CrossrefWeb of ScienceGoogle Scholar

  • [13] Nguyen, H. H. and V. Vu (2014). Random matrices: law of the determinant. Ann. Probab. 42(1), 146–167. Web of ScienceCrossrefGoogle Scholar

  • [14] Weisbin, C. R.,W. Lincoln, and S. Saatchi (2014). A systems engineering approach to estimating uncertainty in above-ground biomass (agb) derived from remote-sensing data. Syst. Engin. 17(3), 361–373. CrossrefGoogle Scholar

About the article

Received: 2016-05-23

Accepted: 2016-07-12

Published Online: 2016-09-23


Citation Information: Dependence Modeling, ISSN (Online) 2300-2298, DOI: https://doi.org/10.1515/demo-2016-0009.

Export Citation

© 2016 Roger M. Cooke et al. . This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Comments (0)

Please log in or register to comment.
Log in