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New Exploratory Tools for Extremal Dependence: $$\chi $$ χ Networks and Annual Extremal Networks

Author

Listed:
  • Whitney K. Huang

    (University of Victoria)

  • Daniel S. Cooley

    (Colorado State University)

  • Imme Ebert-Uphoff

    (Colorado State University)

  • Chen Chen

    (University of Chicago)

  • Snigdhansu Chatterjee

    (University of Minnesota)

Abstract

Understanding dependence structure among extreme values plays an important role in risk assessment in environmental studies. In this work, we propose the $$\chi $$ χ network and the annual extremal network for exploring the extremal dependence structure of environmental processes. A $$\chi $$ χ network is constructed by connecting pairs whose estimated upper tail dependence coefficient, $${{\hat{\chi }}}$$ χ ^ , exceeds a prescribed threshold. We develop an initial $$\chi $$ χ network estimator, and we use a spatial block bootstrap to assess both the bias and variance of our estimator. We then develop a method to correct the bias of the initial estimator by incorporating the spatial structure in $$\chi $$ χ . In addition to the $$\chi $$ χ network, which assesses spatial extremal dependence over an extended period of time, we further introduce an annual extremal network to explore the year-to-year temporal variation of extremal connections. We illustrate the $$\chi $$ χ and the annual extremal networks by analyzing the hurricane season maximum precipitation at the US Gulf Coast and surrounding area. Analysis suggests there exists long distance extremal dependence for precipitation extremes in the study region and the strength of the extremal dependence may depend on some regional scale meteorological conditions, for example, sea surface temperature.

Suggested Citation

  • Whitney K. Huang & Daniel S. Cooley & Imme Ebert-Uphoff & Chen Chen & Snigdhansu Chatterjee, 2019. "New Exploratory Tools for Extremal Dependence: $$\chi $$ χ Networks and Annual Extremal Networks," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(3), pages 484-501, September.
    • Handle: RePEc:spr:jagbes:v:24:y:2019:i:3:d:10.1007_s13253-019-00356-4
    DOI: 10.1007/s13253-019-00356-4
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    References listed on IDEAS

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    1. Segers, Johan, 2012. "Max-stable models for multivariate extremes," LIDAM Reprints ISBA 2012012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Philippe Naveau & Armelle Guillou & Daniel Cooley & Jean Diebolt, 2009. "Modelling pairwise dependence of maxima in space," Biometrika, Biometrika Trust, vol. 96(1), pages 1-17.
    3. Martin Schlather, 2003. "A dependence measure for multivariate and spatial extreme values: Properties and inference," Biometrika, Biometrika Trust, vol. 90(1), pages 139-156, March.
    4. J. L. Wadsworth & J. A. Tawn & A. C. Davison & D. M. Elton, 2017. "Modelling across extremal dependence classes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 149-175, January.
    5. Tsonis, A.A. & Roebber, P.J., 2004. "The architecture of the climate network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 333(C), pages 497-504.
    6. Segers, Johan, 2012. "Max-Stable Models For Multivariate Extremes," LIDAM Discussion Papers ISBA 2012011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. R. Huser & A. C. Davison, 2013. "Composite likelihood estimation for the Brown--Resnick process," Biometrika, Biometrika Trust, vol. 100(2), pages 511-518.
    8. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
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    Cited by:

    1. Junshu Jiang & Jordan Richards & Raphael Huser & David Bolin, 2024. "The Efficient Tail Hypothesis: An Extreme Value Perspective on Market Efficiency," Papers 2408.06661, arXiv.org.
    2. Dorit Hammerling & Brian J. Reich, 2019. "Guest Editors’ Introduction to the Special Issue on “Climate and the Earth System”," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(3), pages 395-397, September.

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