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Spatial Blind Source Separation

Author

Listed:
  • Bachoc, François
  • Genton, Mark G.
  • Nordhausen, Klaus
  • Ruiz-Gazen, Anne
  • Virta, Joni

Abstract

Recently a blind source separation model was suggested for spatial data together with an estimator based on the simultaneous diagonalization of two scatter matrices. The asymptotic properties of this estimator are derived here and a new estimator, based on the joint diagonalization of more than two scatter matrices, is proposed. The limiting properties and merits of the novel estimator are verified in simulation studies. A real data example illustrates the method.

Suggested Citation

  • Bachoc, François & Genton, Mark G. & Nordhausen, Klaus & Ruiz-Gazen, Anne & Virta, Joni, 2019. "Spatial Blind Source Separation," TSE Working Papers 19-998, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:122871
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    References listed on IDEAS

    as
    1. Miettinen, Jari & Nordhausen, Klaus & Oja, Hannu & Taskinen, Sara, 2014. "Deflation-based separation of uncorrelated stationary time series," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 214-227.
    2. Jari Miettinen & Katrin Illner & Klaus Nordhausen & Hannu Oja & Sara Taskinen & Fabian J. Theis, 2016. "Separation of Uncorrelated Stationary time series using Autocovariance Matrices," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 337-354, May.
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    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.
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    7. 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.
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    9. Alan Gelfand & Alexandra Schmidt & Sudipto Banerjee & C. Sirmans, 2004. "Nonstationary multivariate process modeling through spatially varying coregionalization," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 263-312, December.
    10. Bachoc, François, 2014. "Asymptotic analysis of the role of spatial sampling for covariance parameter estimation of Gaussian processes," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 1-35.
    11. Matilainen, Markus & Nordhausen, Klaus & Oja, Hannu, 2015. "New independent component analysis tools for time series," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 80-87.
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    Keywords

    joint diagonalisation; limiting distribution; multivariate random fields; spatial scatter matrices;
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