© 2002 by Biometrika Trust
Spectral methods for nonstationary spatial processes
1 Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695, U.S.Afuentes{at}stat.ncsu.edu
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.
Key Words: Anisotropy; Covariance; Edge effect; Fourier transform; Geostatistics; Kernel smoothing; Periodogram; Spatial statistics; Variogram
Received January 2001. Revised May 2001
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