IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v37y2022i2d10.1007_s00180-021-01134-y.html
   My bibliography  Save this article

Graphical tests of independence for general distributions

Author

Listed:
  • Jiří Dvořák

    (Charles University)

  • Tomáš Mrkvička

    (University of South Bohemia)

Abstract

We propose two model-free, permutation-based tests of independence between a pair of random variables. The tests can be applied to samples from any bivariate distribution: continuous, discrete, or mixture of those, with light tails or heavy tails. Apart from the broad applicability of the tests, their main benefit lies in the graphical interpretation of the test outcome: in case of rejection of the null hypothesis of independence, the combinations of quantiles in the two marginals are indicated for which the deviation from independence is significant. This information can be used to gain more insight into the properties of the observed data and as guidance for proposing more complicated models and hypotheses. We assess the performance of the proposed tests in a simulation study and compare them with several well-established tests of independence. We observe that for monotone dependence structures, the proposed tests are competitive with most benchmark methods. In contrast, for non-monotone dependence structures, the proposed tests usually outperform the benchmark tests. Furthermore, we illustrate the use of the tests and the interpretation of the test outcome in two real datasets consisting of meteorological reports (daily mean temperature and total daily precipitation, having an atomic component at 0 millimeters) and road accidents reports (type of road and the weather conditions, both variables having categorical distribution).

Suggested Citation

  • Jiří Dvořák & Tomáš Mrkvička, 2022. "Graphical tests of independence for general distributions," Computational Statistics, Springer, vol. 37(2), pages 671-699, April.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:2:d:10.1007_s00180-021-01134-y
    DOI: 10.1007/s00180-021-01134-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-021-01134-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-021-01134-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mari Myllymäki & Tomáš Mrkvička & Pavel Grabarnik & Henri Seijo & Ute Hahn, 2017. "Global envelope tests for spatial processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 381-404, March.
    2. Genest C. & Boies J-C., 2003. "Detecting Dependence With Kendall Plots," The American Statistician, American Statistical Association, vol. 57, pages 275-284, November.
    3. Ilaria L. Amerise & Agostino Tarsitano, 2015. "Correction methods for ties in rank correlations," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(12), pages 2584-2596, December.
    4. Marco Scarsini, 1984. "Strong measures of concordance and convergence in probability," Post-Print hal-00542387, HAL.
    5. Yan, Jun, 2007. "Enjoy the Joy of Copulas: With a Package copula," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 21(i04).
    6. Christian Genest & Bruno Rémillard, 2004. "Test of independence and randomness based on the empirical copula process," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 335-369, December.
    7. Marco Scarsini, 1984. "On measures of concordance," Post-Print hal-00542380, HAL.
    8. Naveen N. Narisetty & Vijayan N. Nair, 2016. "Extremal Depth for Functional Data and Applications," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1705-1714, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Plischke, Elmar & Borgonovo, Emanuele, 2019. "Copula theory and probabilistic sensitivity analysis: Is there a connection?," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1046-1059.
    2. Coblenz, Maximilian & Grothe, Oliver & Schreyer, Manuela & Trutschnig, Wolfgang, 2018. "On the length of copula level curves," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 347-365.
    3. Kateřina Koňasová & Jiří Dvořák, 2021. "Stochastic Reconstruction for Inhomogeneous Point Patterns," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 527-547, June.
    4. Edoardo Berton & Lorenzo Mercuri, 2021. "An Efficient Unified Approach for Spread Option Pricing in a Copula Market Model," Papers 2112.11968, arXiv.org, revised Feb 2023.
    5. Liebscher Eckhard, 2017. "Copula-Based Dependence Measures For Piecewise Monotonicity," Dependence Modeling, De Gruyter, vol. 5(1), pages 198-220, August.
    6. Ferreira Helena & Ferreira Marta, 2020. "Multivariate medial correlation with applications," Dependence Modeling, De Gruyter, vol. 8(1), pages 361-372, January.
    7. Vanderford Courtney & Sang Yongli & Dang Xin, 2020. "Two symmetric and computationally efficient Gini correlations," Dependence Modeling, De Gruyter, vol. 8(1), pages 373-395, January.
    8. Dai, Wenlin & Mrkvička, Tomáš & Sun, Ying & Genton, Marc G., 2020. "Functional outlier detection and taxonomy by sequential transformations," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).
    9. Machová Renáta & Korcsmáros Enikő & Marča Roland & Esseová Monika, 2022. "An International Analysis of Consumers’ Consciousness During the Covid-19 Pandemic in Slovakia and Hungary," Folia Oeconomica Stetinensia, Sciendo, vol. 22(1), pages 130-151, June.
    10. Gijbels, Irène & Kika, Vojtěch & Omelka, Marek, 2021. "On the specification of multivariate association measures and their behaviour with increasing dimension," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    11. Fuchs Sebastian, 2016. "A Biconvex Form for Copulas," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-13, February.
    12. Neslehová, Johanna, 2007. "On rank correlation measures for non-continuous random variables," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 544-567, March.
    13. Ghorbani, Mohammad & Vafaei, Nafiseh & Dvořák, Jiří & Myllymäki, Mari, 2021. "Testing the first-order separability hypothesis for spatio-temporal point patterns," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    14. Pandit, Mahesh & Paudel, Krishna P. & Mishra, Ashok K., 2013. "Do Agricultural Subsidies Affect the Labor Allocation Decision? Comparing Parametric and Semiparametric Methods," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 38(01), pages 1-18, April.
    15. Naoyuki Ishimura & Naohiro Yoshida, 2017. "On a measure of dependence for extreme value copulas," EcoMod2017 10311, EcoMod.
    16. Sergio Ortobelli & Tomáš Tichý, 2015. "On the impact of semidefinite positive correlation measures in portfolio theory," Annals of Operations Research, Springer, vol. 235(1), pages 625-652, December.
    17. Antonio Dalessandro & Gareth W. Peters, 2018. "Tensor Approximation of Generalized Correlated Diffusions and Functional Copula Operators," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 237-271, March.
    18. Claudio G. Borroni, 2019. "Mutual association measures," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 571-591, December.
    19. Liebscher Eckhard, 2014. "Copula-based dependence measures," Dependence Modeling, De Gruyter, vol. 2(1), pages 1-16, October.
    20. Jae Youn Ahn & Sebastian Fuchs, 2020. "On Minimal Copulas under the Concordance Order," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 762-780, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:37:y:2022:i:2:d:10.1007_s00180-021-01134-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.