Discrete Dynamics in Nature and Society (Jan 2014)

Spectral Methods in Spatial Statistics

  • Kun Chen,
  • Lianmin Zhang,
  • Maolin Pan

DOI
https://doi.org/10.1155/2014/380392
Journal volume & issue
Vol. 2014

Abstract

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When the spatial location area increases becoming extremely large, it is very difficult, if not possible, to evaluate the covariance matrix determined by the set of location distance even for gridded stationary Gaussian process. To alleviate the numerical challenges, we construct a nonparametric estimator called periodogram of spatial version to represent the sample property in frequency domain, because periodogram requires less computational operation by fast Fourier transform algorithm. Under some regularity conditions on the process, we investigate the asymptotic unbiasedness property of periodogram as estimator of the spectral density function and achieve the convergence rate.