IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v20y1986i1p1-25.html
   My bibliography  Save this article

On detection of the number of signals in presence of white noise

Author

Listed:
  • Zhao, L. C.
  • Krishnaiah, P. R.
  • Bai, Z. D.

Abstract

In this paper, the authors propose procedures for detection of the number of signals in presence of Gaussian white noise under an additive model. This problem is related to the problem of finding the multiplicity of the smallest eigenvalue of the covariance matrix of the observation vector. The methods used in this paper fall within the framework of the model selection procedures using information theoretic criteria. The strong consistency of the estimates of the number of signals, under different situations, is established. Extensions of the results are also discussed when the noise is not necessarily Gaussian. Also, certain information-theoretic criteria are investigated for determination of the multiplicities of various eigenvalues.

Suggested Citation

  • Zhao, L. C. & Krishnaiah, P. R. & Bai, Z. D., 1986. "On detection of the number of signals in presence of white noise," Journal of Multivariate Analysis, Elsevier, vol. 20(1), pages 1-25, October.
    • Handle: RePEc:eee:jmvana:v:20:y:1986:i:1:p:1-25
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(86)90017-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    Citations

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


    Cited by:

    1. Zhao, Lincheng & Peng, Limin, 2002. "Model selection under order restriction," Statistics & Probability Letters, Elsevier, vol. 57(4), pages 301-306, May.
    2. Oda, Ryoya & Suzuki, Yuya & Yanagihara, Hirokazu & Fujikoshi, Yasunori, 2020. "A consistent variable selection method in high-dimensional canonical discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    3. Madhusudan Bhandapy, 1991. "Robust M-estimation of a dispersion matrix with a structure," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(4), pages 689-705, December.
    4. Xuwen Zhu & Yana Melnykov, 2022. "On Finite Mixture Modeling of Change-point Processes," Journal of Classification, Springer;The Classification Society, vol. 39(1), pages 3-22, March.
    5. N. Bansal & M. Bhandary, 1991. "Bayes estimation of number of signals," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(2), pages 227-243, June.
    6. Nakagawa, Tomoyuki & Watanabe, Hiroki & Hyodo, Masashi, 2021. "Kick-one-out-based variable selection method for Euclidean distance-based classifier in high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    7. Bhandary, Madhusudan, 1996. "Test for generalized variance in signal processing," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 155-162, April.
    8. Bai, Zhidong & Silverstein, Jack W., 2022. "A tribute to P.R. Krishnaiah," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    9. L. Zhao & C. Dorea & C. Gonçalves, 2001. "On Determination of the Order of a Markov Chain," Statistical Inference for Stochastic Processes, Springer, vol. 4(3), pages 273-282, October.
    10. Shao‐Hsuan Wang & Chin‐Tsang Chiang, 2020. "Concordance‐based estimation approaches for the optimal sufficient dimension reduction score," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 662-689, September.
    11. Zaka Ratsimalahelo, 2003. "Rank Test Based On Matrix Perturbation Theory," Econometrics 0306008, University Library of Munich, Germany.
    12. Kundu, Debasis & Mitra, Amit, 2001. "Estimating the number of signals of the damped exponential models," Computational Statistics & Data Analysis, Elsevier, vol. 36(2), pages 245-256, April.
    13. d’Artis Kancs & Julda Kielyte, 2002. "Migration in the Enlarged European Union: Empirical Evidence for Labour Mobility in the Baltic States," EERI Research Paper Series EERI_RP_2002_04, Economics and Econometrics Research Institute (EERI), Brussels.
    14. Zhu, Li-Ping & Zhu, Li-Xing, 2007. "On kernel method for sliced average variance estimation," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 970-991, May.
    15. GONZALO, Jesus & PITARAKIS, Jean-Yves, 1994. "Comovements in Large Systems," LIDAM Discussion Papers CORE 1994065, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. Yasunori Fujikoshi & Tetsuro Sakurai, 2023. "High-Dimensional Consistencies of KOO Methods for the Selection of Variables in Multivariate Linear Regression Models with Covariance Structures," Mathematics, MDPI, vol. 11(3), pages 1-15, January.
    17. Zaka Ratsimalahelo, 2003. "Strongly Consistent Determination of the Rank of Matrix," EERI Research Paper Series EERI_RP_2003_04, Economics and Econometrics Research Institute (EERI), Brussels.
    18. Fang, Fang & Yu, Zhou, 2020. "Model averaging assisted sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    19. Zhu, Li-Xing & Ohtaki, Megu & Li, Yingxing, 2007. "On hybrid methods of inverse regression-based algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2621-2635, February.
    20. Kundu, Debasis & Murali, G., 1996. "Model selection in linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 22(5), pages 461-469, September.

    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:jmvana:v:20:y:1986:i:1:p:1-25. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.