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Automatic estimation of spatial spectra via smoothing splines

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  • Shibin Zhang

    (Shanghai Normal University)

Abstract

Spectra are frequently used to depict the dependence features of a second-order stationary process. In this paper, the spatial log-spectral density is expressed by a new type of smoothing splines in the form of the summation of a linear expression of univariate bases and two quadratic forms of univariate bases. Based on this new type of smoothing splines, a Bayesian nonparametric method is proposed to estimate the spectral density of spatial data observed on a lattice. The proposed Bayesian approach uses a Hamiltonian Monte Carlo-within-Gibbs technique to fit smoothing splines to the spatial periodogram. Our technique produces an automatically smoothed spatial spectral estimate along with samples from the posterior distributions of the parameters to facilitate inference.

Suggested Citation

  • Shibin Zhang, 2022. "Automatic estimation of spatial spectra via smoothing splines," Computational Statistics, Springer, vol. 37(2), pages 565-590, April.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:2:d:10.1007_s00180-021-01141-z
    DOI: 10.1007/s00180-021-01141-z
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    References listed on IDEAS

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    1. Zhang, Shibin, 2016. "Adaptive spectral estimation for nonstationary multivariate time series," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 330-349.
    2. Fuentes, Montserrat, 2007. "Approximate Likelihood for Large Irregularly Spaced Spatial Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 321-331, March.
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    8. Robert T. Krafty & Ori Rosen & David S. Stoffer & Daniel J. Buysse & Martica H. Hall, 2017. "Conditional Spectral Analysis of Replicated Multiple Time Series With Application to Nocturnal Physiology," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1405-1416, October.
    9. Robert T. Krafty & William O. Collinge, 2013. "Penalized multivariate Whittle likelihood for power spectrum estimation," Biometrika, Biometrika Trust, vol. 100(2), pages 447-458.
    10. Ori Rosen & David S. Stoffer, 2007. "Automatic estimation of multivariate spectra via smoothing splines," Biometrika, Biometrika Trust, vol. 94(2), pages 335-345.
    11. Heyde, C. C. & Gay, R., 1993. "Smoothed periodogram asymptotics and estimation for processes and fields with possible long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 45(1), pages 169-182, March.
    12. Zhang, Shibin, 2019. "Bayesian copula spectral analysis for stationary time series," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 166-179.
    13. Zhang, Shibin, 2020. "Nonparametric Bayesian inference for the spectral density based on irregularly spaced data," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    14. Ori Rosen & Sally Wood & David S. Stoffer, 2012. "AdaptSPEC: Adaptive Spectral Estimation for Nonstationary Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1575-1589, December.
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    Cited by:

    1. Shirin Nezampour & Alireza Nematollahi & Robert T. Krafty & Mehdi Maadooliat, 2024. "A new approach to nonparametric estimation of multivariate spectral density function using basis expansion," Computational Statistics, Springer, vol. 39(7), pages 3625-3641, December.

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