Skip to main content
SpringerLink
Log in

Efficient Calculation of Kendall’s τ for Interval Data

  • Conference paper
Synergies of Soft Computing and Statistics for Intelligent Data Analysis

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 190))

  • 1593 Accesses

Abstract

Calculation of the strength of dependence in the case of interval data is computation-wise a very demanding task. We consider the case of Kendall’s τ statistic, and calculate approximations of its minimal and maximal values using very easy to compute heuristic approximations. Using Monte Carlo simulations and more accurate calculations based on an evolutionary algorithm we have evaluated the effectiveness of proposed heuristics.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arabas, J.: Evolutionary computation for global optimization – current trends. J. Telecommun. Inf. Technol. 4, 5–10 (2011)

    Google Scholar 

  2. Denœux, T., Masson, M.-H., Hébert, P.A.: Nonparametric rank-based statistics and significance tests for fuzzy data. Fuzzy Set. Syst. 153, 1–28 (2005)

    Article  MATH  Google Scholar 

  3. Genest, C., McKay, R.J.: The joy of copulas: Bivariate distributions with uniform marginals. Am. Stat. 88, 1034–1043 (1986)

    Google Scholar 

  4. Genest, C., Rivest, L.-P.: Statistical inference procedures for bivariate Archimedean copulas. J. Am. Stat. Assoc. 88, 1034–1043 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  5. Hébert, P.-A., Masson, M.H., Denœux, T.: Fuzzy rank correlation between fuzzy numbers. In: Proc. of IFSA World Congress, Istanbul, Turkey, pp. 224–227 (2003)

    Google Scholar 

  6. Hryniewicz, O., Opara, K.: Computation of the measures of dependence for imprecise data. In: New Developments in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, Volume I: Foundations. SRI PAS, Warsaw (in press)

    Google Scholar 

  7. Hryniewicz, O., Szediw, A.: Fuzzy Kendall τ statistic for autocorrelated data. In: Soft Methods for Handling Variability and Imprecision, pp. 155–162. Springer, Berlin (2008)

    Google Scholar 

  8. Nelsen, R.B.: Introduction to Copulas. Springer US, New York (1999)

    MATH  Google Scholar 

  9. Opara, K., Arabas, J.: Differential Mutation Based on Population Covariance Matrix. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI. LNCS, vol. 6238, pp. 114–123. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  10. Price, K.V., Storn, R.M., Lampien, J.A.: Differential evolution a practical approach to global optimization. Natural Computing Series. Springer (2005)

    Google Scholar 

  11. Sklar, A.: Fonctions de répartition à n dimensions et leurs marges. Publications de l’Institut de Statistique de l’Université de Paris 8, 229–231 (1959)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Systems Research Institute, Warsaw, Poland

    Olgierd Hryniewicz & Karol Opara

Authors
  1. Olgierd Hryniewicz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Karol Opara
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Olgierd Hryniewicz .

Editor information

Editors and Affiliations

  1. Faculty of Computer Science, Otto-von-Guericke University of Magdebur, Geb. 29, Raum 008, Universitätsplatz 2, Magdeburg, 39106, Germany

    Rudolf Kruse

  2. , FB Informatik & Informationswissenschaft, University of Konstanz, Konstanz, 78457, Germany

    Michael R. Berthold

  3. of Magdeburg, Faculty of Computer Science, Otto-von-Guericke University, Geb. 29, Universitätsplatz 2 008, Magdeburg, 39106, Germany

    Christian Moewes

  4. , Department of Statistics and OR, University of Oviedo, C/ Calvo Sotelo, s/n, Oviedo, 33007, Spain

    María Ángeles Gil

  5. Systems Research Institute, Polish Academy of Sciences, Newelska 6, Warsaw, 01-447, Poland

    Przemysław Grzegorzewski

  6. Systems Research Institute, Polish Academy of Sciences, Newelska 6, Warsaw, 01-447, Poland

    Olgierd Hryniewicz

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hryniewicz, O., Opara, K. (2013). Efficient Calculation of Kendall’s τ for Interval Data. In: Kruse, R., Berthold, M., Moewes, C., Gil, M., Grzegorzewski, P., Hryniewicz, O. (eds) Synergies of Soft Computing and Statistics for Intelligent Data Analysis. Advances in Intelligent Systems and Computing, vol 190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33042-1_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-33042-1_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33041-4

  • Online ISBN: 978-3-642-33042-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation