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Applications of the Periodogram Method for Perturbed Block Toeplitz Matrices in Statistical Signal Processing

Author

Listed:
  • Jesús Gutiérrez-Gutiérrez

    (Department of Biomedical Engineering and Sciences, Tecnun, University of Navarra, Paseo Manuel Lardizábal 13, 20018 San Sebastián, Spain)

  • Xabier Insausti

    (Department of Biomedical Engineering and Sciences, Tecnun, University of Navarra, Paseo Manuel Lardizábal 13, 20018 San Sebastián, Spain)

  • Marta Zárraga-Rodríguez

    (Department of Biomedical Engineering and Sciences, Tecnun, University of Navarra, Paseo Manuel Lardizábal 13, 20018 San Sebastián, Spain)

Abstract

In this paper, we combine the periodogram method for perturbed block Toeplitz matrices with the Cholesky decomposition to give a parameter estimation method for any perturbed vector autoregressive (VAR) or vector moving average (VMA) process, when we only know a perturbed version of the sequence of correlation matrices of the process. In order to combine the periodogram method for perturbed block Toeplitz matrices with the Cholesky decomposition, we first need to generalize a known result on the Cholesky decomposition of Toeplitz matrices to perturbed block Toeplitz matrices.

Suggested Citation

  • Jesús Gutiérrez-Gutiérrez & Xabier Insausti & Marta Zárraga-Rodríguez, 2020. "Applications of the Periodogram Method for Perturbed Block Toeplitz Matrices in Statistical Signal Processing," Mathematics, MDPI, vol. 8(4), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:582-:d:345370
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