IDEAS home Printed from https://ideas.repec.org/p/eca/wpaper/2013-368952.html
   My bibliography  Save this paper

Consistent Distribution–Free Affine–Invariant Tests for the Validity of Independent Component Models

Author

Listed:
  • Marc Hallin
  • Simos Meintanis
  • Klaus Nordhausen

Abstract

We propose a family of tests of the validity of the assumptions underlying independent component analysis methods. The tests are formulated as L2–type procedures based on characteristic functions and involve weights; a proper choice of these weights and the estimation method for the mixing matrix yields consistent and affine-invariant tests. Due to the complexity of the asymptotic null distribution of the resulting test statistics, implementation is based on permutational and resampling strategies. This leads to distribution-free procedures regardless of whether these procedures are performed on the estimated independent components themselves or the componentwise ranks of their components. A Monte Carlo study involving various estimation methods for the mixing matrix, various weights, and a competing test based on distance covariance is conducted under the null hypothesis as well as under alternatives. A real-data application demonstrates the practical utility and effectiveness of the method.

Suggested Citation

  • Marc Hallin & Simos Meintanis & Klaus Nordhausen, 2024. "Consistent Distribution–Free Affine–Invariant Tests for the Validity of Independent Component Models," Working Papers ECARES 2024-04, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:eca:wpaper:2013/368952
    as

    Download full text from publisher

    File URL: https://dipot.ulb.ac.be/dspace/bitstream/2013/368952/3/2024-04-HALLIN_MEINTANIS_NORDHAUSEN.pdf
    File Function: Œuvre complète ou partie de l'œuvre
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gouriéroux, Christian & Monfort, Alain & Renne, Jean-Paul, 2017. "Statistical inference for independent component analysis: Application to structural VAR models," Journal of Econometrics, Elsevier, vol. 196(1), pages 111-126.
    2. Giacomini, Raffaella & Politis, Dimitris N. & White, Halbert, 2013. "A Warp-Speed Method For Conducting Monte Carlo Experiments Involving Bootstrap Estimators," Econometric Theory, Cambridge University Press, vol. 29(3), pages 567-589, June.
    3. Helmut Herwartz & Simone Maxand, 2020. "Nonparametric tests for independence: a review and comparative simulation study with an application to malnutrition data in India," Statistical Papers, Springer, vol. 61(5), pages 2175-2201, October.
    4. Fan, Yanan & de Micheaux, Pierre Lafaye & Penev, Spiridon & Salopek, Donna, 2017. "Multivariate nonparametric test of independence," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 189-210.
    5. Jari Miettinen & Markus Matilainen & Klaus Nordhausen & Sara Taskinen, 2020. "Extracting Conditionally Heteroskedastic Components using Independent Component Analysis," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 293-311, March.
    6. Chen, Feifei & Meintanis, Simos G. & Zhu, Lixing, 2019. "On some characterizations and multidimensional criteria for testing homogeneity, symmetry and independence," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 125-144.
    7. Shubhadeep Chakraborty & Xianyang Zhang, 2019. "Distance Metrics for Measuring Joint Dependence with Application to Causal Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(528), pages 1638-1650, October.
    8. García-Ferrer, Antonio & González-Prieto, Ester & Peña, Daniel, 2012. "A conditionally heteroskedastic independent factor model with an application to financial stock returns," International Journal of Forecasting, Elsevier, vol. 28(1), pages 70-93.
    9. C Genest & J G Nešlehová & B Rémillard & O A Murphy, 2019. "Testing for independence in arbitrary distributions," Biometrika, Biometrika Trust, vol. 106(1), pages 47-68.
    10. Dominic Edelmann & Konstantinos Fokianos & Maria Pitsillou, 2019. "An Updated Literature Review of Distance Correlation and Its Applications to Time Series," International Statistical Review, International Statistical Institute, vol. 87(2), pages 237-262, August.
    11. Tran Hoang Hai, 2020. "Estimation of volatility causality in structural autoregressions with heteroskedasticity using independent component analysis," Statistical Papers, Springer, vol. 61(1), pages 1-16, February.
    12. Kozubowski, Tomasz J. & Podgórski, Krzysztof & Rychlik, Igor, 2013. "Multivariate generalized Laplace distribution and related random fields," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 59-72.
    13. Sirkku Pauliina Ilmonen & Davy Paindaveine, 2011. "Semiparametrically Efficient Inference Based on Signed Ranks in Symmetric Independent Component Models," Working Papers ECARES ECARES 2011-003, ULB -- Universite Libre de Bruxelles.
    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. Meintanis, Simos G. & Hušková, Marie & Hlávka, Zdeněk, 2022. "Fourier-type tests of mutual independence between functional time series," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    2. Hušková, Marie & Meintanis, Simos G. & Pretorius, Charl, 2020. "Tests for validity of the semiparametric heteroskedastic transformation model," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    3. Beaulieu Guillaume Boglioni & de Micheaux Pierre Lafaye & Ouimet Frédéric, 2021. "Counterexamples to the classical central limit theorem for triplewise independent random variables having a common arbitrary margin," Dependence Modeling, De Gruyter, vol. 9(1), pages 424-438, January.
    4. Dante Amengual & Gabriele Fiorentini & Enrique Sentana, 2022. "Moment tests of independent components," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 13(1), pages 429-474, May.
    5. Nasri, Bouchra R., 2022. "Tests of serial dependence for multivariate time series with arbitrary distributions," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    6. Herwartz, Helmut & Wang, Shu, 2023. "Point estimation in sign-restricted SVARs based on independence criteria with an application to rational bubbles," Journal of Economic Dynamics and Control, Elsevier, vol. 151(C).
    7. Zdeněk Hlávka & Marie Hušková & Simos G. Meintanis, 2020. "Change-point methods for multivariate time-series: paired vectorial observations," Statistical Papers, Springer, vol. 61(4), pages 1351-1383, August.
    8. Moneta, Alessio & Pallante, Gianluca, 2022. "Identification of Structural VAR Models via Independent Component Analysis: A Performance Evaluation Study," Journal of Economic Dynamics and Control, Elsevier, vol. 144(C).
    9. Fiorentini, Gabriele & Sentana, Enrique, 2023. "Discrete mixtures of normals pseudo maximum likelihood estimators of structural vector autoregressions," Journal of Econometrics, Elsevier, vol. 235(2), pages 643-665.
    10. Fernández-Durán Juan José & Gregorio-Domínguez María Mercedes, 2023. "Test of bivariate independence based on angular probability integral transform with emphasis on circular-circular and circular-linear data," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-17, January.
    11. Bernd Funovits, 2019. "Identification and Estimation of SVARMA models with Independent and Non-Gaussian Inputs," Papers 1910.04087, arXiv.org.
    12. Roy, Angshuman & Ghosh, Anil K., 2020. "Some tests of independence based on maximum mean discrepancy and ranks of nearest neighbors," Statistics & Probability Letters, Elsevier, vol. 164(C).
    13. Jari Miettinen & Katrin Illner & Klaus Nordhausen & Hannu Oja & Sara Taskinen & Fabian J. Theis, 2016. "Separation of Uncorrelated Stationary time series using Autocovariance Matrices," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 337-354, May.
    14. Sangyeol Lee & Simos G. Meintanis & Minyoung Jo, 2019. "Inferential procedures based on the integrated empirical characteristic function," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 357-386, September.
    15. Zdeněk Hlávka & Marie Hušková & Simos G. Meintanis, 2021. "Testing serial independence with functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 603-629, September.
    16. Sebastiano Michele Zema, 2020. "Directed Acyclic Graph based Information Shares for Price Discovery," LEM Papers Series 2020/28, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    17. Chen, Feifei & Meintanis, Simos G. & Zhu, Lixing, 2019. "On some characterizations and multidimensional criteria for testing homogeneity, symmetry and independence," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 125-144.
    18. Bernd Funovits, 2020. "Identifiability and Estimation of Possibly Non-Invertible SVARMA Models: A New Parametrisation," Papers 2002.04346, arXiv.org, revised Feb 2021.
    19. Chen, Feifei & Jiménez–Gamero, M. Dolores & Meintanis, Simos & Zhu, Lixing, 2022. "A general Monte Carlo method for multivariate goodness–of–fit testing applied to elliptical families," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    20. Guerini, Mattia & Moneta, Alessio & Napoletano, Mauro & Roventini, Andrea, 2020. "The Janus-Faced Nature Of Debt: Results From A Data-Driven Cointegrated Svar Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 24(1), pages 24-54, January.

    More about this item

    Keywords

    Characteristic function; total independence; independent component model; rank test;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:eca:wpaper:2013/368952. 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: Benoit Pauwels (email available below). General contact details of provider: https://edirc.repec.org/data/arulbbe.html .

    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.