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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 380392, 6 pages
Research Article

Spectral Methods in Spatial Statistics

1School of Statistics, Southwestern University of Finance and Economics, Chengdu 611130, China
2School of Management and Engineering, Nanjing University, Nanjing 210093, China
3Department of Mathematics, Nanjing University, Nanjing 210093, China

Received 2 April 2014; Accepted 27 May 2014; Published 15 June 2014

Academic Editor: Xiaolin Xu

Copyright © 2014 Kun Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.