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On detection of the number of signals when the noise covariance matrix is arbitrary

Author

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

Abstract

In this paper, the authors proposed model selection methods for determination of the number of signals in presence of noise with arbitrary covariance matrix. This problem is related to finding the multiplicity of the smallest eigenvalue of [Sigma]2[Sigma]1-1, where [Sigma]2 = [Gamma] + [lambda][Sigma]1, [Sigma]1 and [Sigma]2 are covariance matrices, [lambda] is a scalar, and [Gamma] is non-negative definite matrix and is not of full rank. Also, the authors proposed methods for determination of the multiplicities of various eigenvalues of [Sigma]2[Sigma]1-1. The methods used in these procedures are based upon certain information theoretic criteria. The strong consistency of these criteria is established in this paper.

Suggested Citation

  • Zhao, L. C. & Krishnaiah, P. R. & Bai, Z. D., 1986. "On detection of the number of signals when the noise covariance matrix is arbitrary," Journal of Multivariate Analysis, Elsevier, vol. 20(1), pages 26-49, October.
    • Handle: RePEc:eee:jmvana:v:20:y:1986:i:1:p:26-49
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    Citations

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    Cited by:

    1. 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.
    2. Samuel Müller & Alan H. Welsh, 2010. "On Model Selection Curves," International Statistical Review, International Statistical Institute, vol. 78(2), pages 240-256, August.
    3. Bhandary, Madhusudan, 1996. "Test for generalized variance in signal processing," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 155-162, April.
    4. Bai, Zhidong & Silverstein, Jack W., 2022. "A tribute to P.R. Krishnaiah," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    5. 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.
    6. 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.
    7. I. M. Johnstone & B. Nadler, 2017. "Roy’s largest root test under rank-one alternatives," Biometrika, Biometrika Trust, vol. 104(1), pages 181-193.
    8. 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.
    9. 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.
    10. Guyon, Xavier & Yao, Jian-feng, 1999. "On the Underfitting and Overfitting Sets of Models Chosen by Order Selection Criteria," Journal of Multivariate Analysis, Elsevier, vol. 70(2), pages 221-249, August.

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