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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
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    Citations

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    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. 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.
    3. 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.
    4. 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.
    5. Zaka Ratsimalahelo, 2003. "Rank Test Based On Matrix Perturbation Theory," Econometrics 0306008, University Library of Munich, Germany.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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).
    11. Fang, Fang & Yu, Zhou, 2020. "Model averaging assisted sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    12. 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).
    13. 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.
    14. 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).
    15. Bhandary, Madhusudan, 1996. "Test for generalized variance in signal processing," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 155-162, April.
    16. Bai, Zhidong & Silverstein, Jack W., 2022. "A tribute to P.R. Krishnaiah," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    17. 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.
    18. Yana Melnykov & Marcus Perry, 2024. "On Robust Change Point Detection and Estimation in Multisubject Studies," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(2), pages 827-879, August.
    19. 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.
    20. Joni Virta & Niko Lietzén & Henri Nyberg, 2024. "Robust signal dimension estimation via SURE," Statistical Papers, Springer, vol. 65(5), pages 3007-3038, July.
    21. 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.
    22. Kundu, Debasis & Murali, G., 1996. "Model selection in linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 22(5), pages 461-469, September.

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