IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v131y2019icp116-130.html
   My bibliography  Save this article

A significance test of the RV coefficient in high dimensions

Author

Listed:
  • Rauf Ahmad, M.

Abstract

The RV coefficient is an important measure of linear dependence between two multivariate data vectors. Using unbiased and computationally efficient estimators of its components, a modification to the RV coefficient is proposed, and used to construct a test of significance for the true coefficient. The modified estimator improves the accuracy of the original and, along with the test, can be applied to data with arbitrarily large dimensions, possibly exceeding the sample size, and the underlying distribution need only have finite fourth moment. Exact and asymptotic properties are studied under fairly general conditions. The accuracy of the modified estimator and the test is shown through simulations under a variety of parameter settings. In comparisons against several existing methods, both the proposed estimator and the test exhibit similar performance to the distance correlation. Several real data applications are also provided.

Suggested Citation

  • Rauf Ahmad, M., 2019. "A significance test of the RV coefficient in high dimensions," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 116-130.
    • Handle: RePEc:eee:csdana:v:131:y:2019:i:c:p:116-130
    DOI: 10.1016/j.csda.2018.10.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947318302536
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2018.10.008?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. Lavit, Christine & Escoufier, Yves & Sabatier, Robert & Traissac, Pierre, 1994. "The ACT (STATIS method)," Computational Statistics & Data Analysis, Elsevier, vol. 18(1), pages 97-119, August.
    2. Székely, Gábor J. & Rizzo, Maria L., 2013. "The distance correlation t-test of independence in high dimension," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 193-213.
    3. Xiang Zhan & Anna Plantinga & Ni Zhao & Michael C. Wu, 2017. "A fast small‐sample kernel independence test for microbiome community‐level association analysis," Biometrics, The International Biometric Society, vol. 73(4), pages 1453-1463, December.
    4. Robert, P. & Cleroux, R. & Ranger, N., 1985. "Some results on vector correlation," Computational Statistics & Data Analysis, Elsevier, vol. 3(1), pages 25-32, May.
    5. Kazi-Aoual, Frederique & Hitier, Simon & Sabatier, Robert & Lebreton, Jean-Dominique, 1995. "Refined approximations to permutation tests for multivariate inference," Computational Statistics & Data Analysis, Elsevier, vol. 20(6), pages 643-656, December.
    6. M. Rauf Ahmad, 2017. "Location-invariant Multi-sample U-tests for Covariance Matrices with Large Dimension," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 500-523, June.
    7. Jérôme Allaire & Yves Lepage, 1992. "A procedure for assessing vector correlations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(4), pages 755-768, December.
    8. P. Robert & Y. Escoufier, 1976. "A Unifying Tool for Linear Multivariate Statistical Methods: The RV‐Coefficient," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 25(3), pages 257-265, November.
    9. Josse, J. & Pagès, J. & Husson, F., 2008. "Testing the significance of the RV coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 82-91, September.
    10. M. Ahmad, 2014. "A $$U$$ -statistic approach for a high-dimensional two-sample mean testing problem under non-normality and Behrens–Fisher setting," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 33-61, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ahmad, Rauf, 2022. "Tests for proportionality of matrices with large dimension," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

    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. Bavaud, François, 2023. "Exact first moments of the RV coefficient by invariant orthogonal integration," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    2. Xiang Zhan & Anna Plantinga & Ni Zhao & Michael C. Wu, 2017. "A fast small‐sample kernel independence test for microbiome community‐level association analysis," Biometrics, The International Biometric Society, vol. 73(4), pages 1453-1463, December.
    3. Mayer Claus-Dieter & Lorent Julie & Horgan Graham W, 2011. "Exploratory Analysis of Multiple Omics Datasets Using the Adjusted RV Coefficient," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-27, March.
    4. Figueiredo, Adelaide & Figueiredo, Fernanda & Monteiro, Natália P. & Straume, Odd Rune, 2012. "Restructuring in privatised firms: A Statis approach," Structural Change and Economic Dynamics, Elsevier, vol. 23(1), pages 108-116.
    5. Jean-Pierre Rossi & Maxime Nardin & Martin Godefroid & Manuela Ruiz-Diaz & Anne-Sophie Sergent & Alejandro Martinez-Meier & Luc Pâques & Philippe Rozenberg, 2014. "Dissecting the Space-Time Structure of Tree-Ring Datasets Using the Partial Triadic Analysis," PLOS ONE, Public Library of Science, vol. 9(9), pages 1-13, September.
    6. Yongshuai Chen & Wenwen Guo & Hengjian Cui, 2024. "On the test of covariance between two high-dimensional random vectors," Statistical Papers, Springer, vol. 65(5), pages 2687-2717, July.
    7. Mansooreh Kazemilari & Maman Abdurachman Djauhari & Zuhaimy Ismail, 2016. "Foreign Exchange Market Performance: Evidence from Bivariate Time Series Approach," Papers 1608.07694, arXiv.org.
    8. Rauf Ahmad, M. & Pavlenko, Tatjana, 2018. "A U-classifier for high-dimensional data under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 269-283.
    9. Hyodo, Masashi & Nishiyama, Takahiro & Pavlenko, Tatjana, 2020. "Testing for independence of high-dimensional variables: ρV-coefficient based approach," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    10. Josse, J. & Pagès, J. & Husson, F., 2008. "Testing the significance of the RV coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 82-91, September.
    11. Górecki Tomasz & Krzyśko Mirosław & Ratajczak Waldemar & Wołyński Waldemar, 2016. "An Extension of the Classical Distance Correlation Coefficient for Multivariate Functional Data with Applications," Statistics in Transition New Series, Statistics Poland, vol. 17(3), pages 449-466, September.
    12. Svetlana V Shinkareva & Robert A Mason & Vicente L Malave & Wei Wang & Tom M Mitchell & Marcel Adam Just, 2008. "Using fMRI Brain Activation to Identify Cognitive States Associated with Perception of Tools and Dwellings," PLOS ONE, Public Library of Science, vol. 3(1), pages 1-9, January.
    13. Patrick Wolf & Tobias Buchmann, 2021. "Analyzing development patterns in research networks and technology," Review of Evolutionary Political Economy, Springer, vol. 2(1), pages 55-81, April.
    14. Parraguez, Pedro & Škec, Stanko & e Carmo, Duarte Oliveira & Maier, Anja, 2020. "Quantifying technological change as a combinatorial process," Technological Forecasting and Social Change, Elsevier, vol. 151(C).
    15. Carmen C. Rodríguez-Martínez & Mitzi Cubilla-Montilla & Purificación Vicente-Galindo & Purificación Galindo-Villardón, 2021. "Sparse STATIS-Dual via Elastic Net," Mathematics, MDPI, vol. 9(17), pages 1-15, August.
    16. Sergio Camiz & Valério D. Pillar, 2018. "Identifying the Informational/Signal Dimension in Principal Component Analysis," Mathematics, MDPI, vol. 6(11), pages 1-16, November.
    17. Ahmad, Rauf, 2022. "Tests for proportionality of matrices with large dimension," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    18. Mariela González-Narváez & María José Fernández-Gómez & Susana Mendes & José-Luis Molina & Omar Ruiz-Barzola & Purificación Galindo-Villardón, 2021. "Study of Temporal Variations in Species–Environment Association through an Innovative Multivariate Method: MixSTATICO," Sustainability, MDPI, vol. 13(11), pages 1-25, May.
    19. Marta de la Cuesta-González & Cristina Ruza & José M. Rodríguez-Fernández, 2020. "Rethinking the Income Inequality and Financial Development Nexus. A Study of Nine OECD Countries," Sustainability, MDPI, vol. 12(13), pages 1-18, July.
    20. Pietro Amenta & Antonio Lucadamo & Antonello D’Ambra, 2021. "Restricted Common Component and Specific Weight Analysis: A Constrained Explorative Approach for the Customer Satisfaction Evaluation," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 156(2), pages 409-427, August.

    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:eee:csdana:v:131:y:2019:i:c:p:116-130. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.