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A Test for Truncation Invariant Dependence

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Soft Methods for Data Science (SMPS 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 456))

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Abstract

A test is proposed to check whether a random sample comes from a truncation invariant copula C, that is, if C is the copula of a pair (U, V) of random variables uniformly distributed on [0, 1], then C is also the copula of the conditional distribution function of \((U,V\mid U\le \alpha )\) for every \(\alpha \in (0,1]\). The asymptotic normality of the test statistics is shown. Moreover, a procedure is described to simplify the approximation of the asymptotic variance of the test. Its performance is investigated in a simulation study.

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Acknowledgments

We would like to thank Bruno Rémillard for many useful comments about the asymptotic behavior of our test procedure. The authors have been supported by Free University of Bozen-Bolzano, Italy, via the projects COCCO and MODEX. The third author acknowledges the support from National Science Centre, Poland, under project 2015/17/B/HS4/00911.

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Authors and Affiliations

  1. Free University of Bozen-Bolzano, Bolzano, Italy

    F. Marta L. Di Lascio & Fabrizio Durante

  2. University of Warsaw, Warsaw, Poland

    Piotr Jaworski

Authors
  1. F. Marta L. Di Lascio
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  2. Fabrizio Durante
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  3. Piotr Jaworski
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Corresponding author

Correspondence to Piotr Jaworski .

Editor information

Editors and Affiliations

  1. Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy

    Maria Brigida Ferraro

  2. Department of Statistical Sciences, Sapienza University of Rome, Roma, Italy

    Paolo Giordani

  3. Dept of Basic & Applied Sciences Engg, Sapienza University of Rome, Rome, Italy

    Barbara Vantaggi

  4. Dept of Stoc Metds,Polish Academy of Sci, Systems Research Institute, Warsaw, Poland

    Marek Gagolewski

  5. Dept of Statis&OR and MD, Univ de Oviedo, Oviedo, Spain

    María Ángeles Gil

  6. Dept of Stoc Metds,Polish Aca of Science, Systems Res Inst, Warsaw, Poland

    Przemysław Grzegorzewski

  7. Sys Res Inti, Dept of Stoch Methods, Polish Acadmy Sci in Warsaw, Warsaw, Poland

    Olgierd Hryniewicz

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Di Lascio, F.M.L., Durante, F., Jaworski, P. (2017). A Test for Truncation Invariant Dependence. In: Ferraro, M., et al. Soft Methods for Data Science. SMPS 2016. Advances in Intelligent Systems and Computing, vol 456. Springer, Cham. https://doi.org/10.1007/978-3-319-42972-4_22

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  • DOI: https://doi.org/10.1007/978-3-319-42972-4_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42971-7

  • Online ISBN: 978-3-319-42972-4

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