IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v83y2013i4p1219-1226.html
   My bibliography  Save this article

On asymptotic properties of the scatter matrix based estimates for complex valued independent component analysis

Author

Listed:
  • Ilmonen, Pauliina

Abstract

In this paper, we consider the independent component (IC) model, and the asymptotic properties of the complex valued unmixing matrix estimates that are based on simultaneous use of two scatter matrix functionals.

Suggested Citation

  • Ilmonen, Pauliina, 2013. "On asymptotic properties of the scatter matrix based estimates for complex valued independent component analysis," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1219-1226.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:4:p:1219-1226
    DOI: 10.1016/j.spl.2013.01.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715213000217
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2013.01.020?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Sirkiä, Seija & Taskinen, Sara & Oja, Hannu, 2007. "Symmetrised M-estimators of multivariate scatter," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1611-1629, September.
    2. Roelant, E. & Van Aelst, S. & Croux, C., 2009. "Multivariate generalized S-estimators," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 876-887, May.
    3. Pauliina Ilmonen & Hannu Oja & Robert Serfling, 2012. "On Invariant Coordinate System (ICS) Functionals," International Statistical Review, International Statistical Institute, vol. 80(1), pages 93-110, April.
    4. David E. Tyler & Frank Critchley & Lutz Dümbgen & Hannu Oja, 2009. "Invariant co‐ordinate selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 549-592, June.
    5. Ilmonen, Pauliina & Nevalainen, Jaakko & Oja, Hannu, 2010. "Characteristics of multivariate distributions and the invariant coordinate system," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1844-1853, December.
    6. Ollila, Esa & Oja, Hannu & Koivunen, Visa, 2008. "Complex-valued ICA based on a pair of generalized covariance matrices," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3789-3805, March.
    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. Lietzén, Niko & Nordhausen, Klaus & Ilmonen, Pauliina, 2016. "Minimum distance index for complex valued ICA," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 100-106.
    2. Lee, Seonjoo & Shen, Haipeng & Truong, Young, 2021. "Sampling properties of color Independent Component Analysis," Journal of Multivariate Analysis, Elsevier, vol. 181(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. Nordhausen, Klaus & Ruiz-Gazen, Anne, 2022. "On the usage of joint diagonalization in multivariate statistics," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. Archimbaud, Aurore & Boulfani, Feriel & Gendre, Xavier & Nordhausen, Klaus & Ruiz-Gazen, Anne & Virta, Joni, 2025. "ICS for multivariate functional anomaly detection with applications to predictive maintenance and quality control," Econometrics and Statistics, Elsevier, vol. 33(C), pages 282-303.
    3. Dürre, Alexander & Vogel, Daniel & Tyler, David E., 2014. "The spatial sign covariance matrix with unknown location," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 107-117.
    4. Dümbgen, Lutz & Nordhausen, Klaus & Schuhmacher, Heike, 2016. "New algorithms for M-estimation of multivariate scatter and location," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 200-217.
    5. Loperfido, Nicola, 2015. "Vector-valued skewness for model-based clustering," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 230-237.
    6. Xin Dang & Hailin Sang & Lauren Weatherall, 2019. "Gini covariance matrix and its affine equivariant version," Statistical Papers, Springer, vol. 60(3), pages 641-666, June.
    7. Lee, Seonjoo & Shen, Haipeng & Truong, Young, 2021. "Sampling properties of color Independent Component Analysis," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    8. Sreenivasa Rao Jammalamadaka & Emanuele Taufer & György H. Terdik, 2021. "Asymptotic theory for statistics based on cumulant vectors with applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 708-728, June.
    9. Loperfido, Nicola, 2021. "Some theoretical properties of two kurtosis matrices, with application to invariant coordinate selection," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    10. Miettinen, Jari & Nordhausen, Klaus & Oja, Hannu & Taskinen, Sara, 2012. "Statistical properties of a blind source separation estimator for stationary time series," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1865-1873.
    11. François Bachoc & Marc G Genton & Klaus Nordhausen & Anne Ruiz-Gazen & Joni Virta, 2020. "Spatial blind source separation," Biometrika, Biometrika Trust, vol. 107(3), pages 627-646.
    12. Virta, Joni & Lietzén, Niko & Viitasaari, Lauri & Ilmonen, Pauliina, 2024. "Latent model extreme value index estimation," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    13. Alashwali, Fatimah & Kent, John T., 2016. "The use of a common location measure in the invariant coordinate selection and projection pursuit," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 145-161.
    14. Fischer, Daniel & Berro, Alain & Nordhausen, Klaus & Ruiz-Gazen, Anne, 2019. "REPPlab: An R package for detecting clusters and outliers using exploratory projection pursuit," TSE Working Papers 19-1001, Toulouse School of Economics (TSE).
    15. Roelant, E. & Van Aelst, S. & Croux, C., 2009. "Multivariate generalized S-estimators," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 876-887, May.
    16. Joni Virta & Niko Lietzén & Henri Nyberg, 2024. "Robust signal dimension estimation via SURE," Statistical Papers, Springer, vol. 65(5), pages 3007-3038, July.
    17. Lutz Dümbgen & Klaus Nordhausen, 2024. "Approximating symmetrized estimators of scatter via balanced incomplete U-statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(2), pages 185-207, April.
    18. Ruiz-Gazen, Anne & Thomas-Agnan, Christine & Laurent, Thibault & Mondon, Camille, 2022. "Detecting outliers in compositional data using Invariant Coordinate Selection," TSE Working Papers 22-1320, Toulouse School of Economics (TSE).
    19. Nicola Loperfido, 2019. "Finite mixtures, projection pursuit and tensor rank: a triangulation," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(1), pages 145-173, March.
    20. Salibian-Barrera, Matias & Van Aelst, Stefan & Yohai, Víctor J., 2016. "Robust tests for linear regression models based on τ-estimates," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 436-455.

    More about this item

    Keywords

    ;
    ;
    ;

    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:eee:stapro:v:83:y:2013:i:4:p:1219-1226. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.