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Econometrics of Risk pp 161–169Cite as

Local Kendall’s Tau

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Part of the book series: Studies in Computational Intelligence ((SCI,volume 583))

Abstract

We introduce two local versions of Kendall’s tau conditioning on one or two random variable(s) varying less than a fixed distance. Some basic properties are proved. These local Kendall’s taus are computed for some shuffles of Min and the Farlie-Gumbel-Morgenstern copulas and shown to distinguish between complete dependence and independence copulas. A pointwise version of Kendall’s tau is also proposed and shown to distinguish between comonotonicity and countermonotonicity for complete dependence copulas.

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Notes

  1. 1.

    \(L_1 = [\max (0,\alpha +a,\alpha -1+b),\min (\alpha ,1+a,b)]\cup [\max (0,a,b),\min (\alpha ,\alpha +a,\alpha +b)]\cup [\max (0,\alpha +a,b),\min (\alpha ,1+a,b+\alpha )]\cup [\max (0,1+a,\alpha -1+b),\min (\alpha ,b+\alpha )]\cup [\max (0,\alpha +b,a),\min (\alpha ,1+a)]\cup [\max (0,\alpha +b,1+a),\alpha ]\) and \(L_2 = [\max (1-\alpha ,\alpha +a,\alpha +b),\min (1,1+a,1+b)]\cup [\max (1-\alpha ,a,1+b),\min (1,\alpha +a,\alpha +1+b)]\cup [\max (1-\alpha ,\alpha +a,1+b),\min (1,1+a,\alpha +1+b)]\cup [\max (1-\alpha ,1+a,\alpha +b),\min (1,\alpha +1+b)]\cup [\max (1-\alpha ,a,\alpha +1+b),\min (1,1+a)]\cup [\max (1-\alpha ,1+a,\alpha +1+b),1]\).

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Acknowledgments

The authors thank the anonymous referee for comments and suggestions. The last author would also like to thank the Commission on Higher Education and the Thailand Research Fund for the support through grant no. RSA5680037.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok, Thailand

    P. Buthkhunthong, A. Junchuay, I. Ongeera, T. Santiwipanont & S. Sumetkijakan

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  1. P. Buthkhunthong
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  2. A. Junchuay
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  3. I. Ongeera
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  4. T. Santiwipanont
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  5. S. Sumetkijakan
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Corresponding author

Correspondence to S. Sumetkijakan .

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Editors and Affiliations

  1. Japan Advanced Institute of Science and Technology, Nomi, Japan

    Van-Nam Huynh

  2. Department of Computer Science, University of Texas at El Paso, El Paso, Texas, USA

    Vladik Kreinovich

  3. Faculty of Economics, Chiang Mai University, Chiang Mai, Thailand

    Songsak Sriboonchitta

  4. Faculty of Economics, Chiang Mai University, Chiang Mai, Thailand

    Komsan Suriya

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Buthkhunthong, P., Junchuay, A., Ongeera, I., Santiwipanont, T., Sumetkijakan, S. (2015). Local Kendall’s Tau. In: Huynh, VN., Kreinovich, V., Sriboonchitta, S., Suriya, K. (eds) Econometrics of Risk. Studies in Computational Intelligence, vol 583. Springer, Cham. https://doi.org/10.1007/978-3-319-13449-9_11

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  • DOI: https://doi.org/10.1007/978-3-319-13449-9_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13448-2

  • Online ISBN: 978-3-319-13449-9

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