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Spectral methods for nonstationary spatial processes

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  • Montserrat Fuentes
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    Abstract

    We propose a nonstationary periodogram and various parametric approaches for estimating the spectral density of a nonstationary spatial process. We also study the asymptotic properties of the proposed estimators via shrinking asymptotics, assuming the distance between neighbouring observations tends to zero as the size of the observation region grows without bound. With this type of asymptotic model we can uniquely determine the spectral density, avoiding the aliasing problem. We also present a new class of nonstationary processes, based on a convolution of local stationary processes. This model has the advantage that the model is simultaneously defined everywhere, unlike 'moving window' approaches, but it retains the attractive property that, locally in small regions, it behaves like a stationary spatial process. Applications include the spatial analysis and modelling of air pollution data provided by the US Environmental Protection Agency. Copyright Biometrika Trust 2002, Oxford University Press.

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    Bibliographic Info

    Article provided by Biometrika Trust in its journal Biometrika.

    Volume (Year): 89 (2002)
    Issue (Month): 1 (March)
    Pages: 197-210

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    Handle: RePEc:oup:biomet:v:89:y:2002:i:1:p:197-210

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    Cited by:
    1. 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, vol. 13(2), pages 263-312, December.
    2. Kelejian, Harry H. & Prucha, Ingmar R., 2007. "HAC estimation in a spatial framework," Journal of Econometrics, Elsevier, vol. 140(1), pages 131-154, September.
    3. Chiranjit Mukherjee & Prasad Kasibhatla & Mike West, 2014. "Spatially varying SAR models and Bayesian inference for high-resolution lattice data," Annals of the Institute of Statistical Mathematics, Springer, vol. 66(3), pages 473-494, June.
    4. Whitcher, Brandon, 2006. "Wavelet-based bootstrapping of spatial patterns on a finite lattice," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2399-2421, May.
    5. Fernández-Avilés, G & Montero, JM & Mateu, J, 2011. "Mathematical Genesis of the Spatio-Temporal Covariance Functions," MPRA Paper 35874, University Library of Munich, Germany.
    6. Lim, Chae Young & Stein, Michael, 2008. "Properties of spatial cross-periodograms using fixed-domain asymptotics," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1962-1984, October.

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