Statistical Modelling 2 (2002), 267–279
Interpolation of nonstationary air pollution processes: a spatial
spectral approach
Montserrat Fuentes,
Statistics Department, North Carolina State University,
Raleigh, NC 27695-8203
USA
eMail: fuentes@stat.ncsu.edu
Abstract:
Spatial processes are important models for many
environmental problems.
Classical geostatistics and Fourier spectral methods
are powerful tools to study the spatial structure of
stationary processes.
However, it is widely recognized that in real applications spatial processes
are rarely stationary and isotropic.
Consequently, it is important to extend
these spectral methods
to processes that are nonstationary.
In this work, we present some new spectral approaches and tools
to estimate the spatial structure of a nonstationary
process.
More specifically, we propose an approach for the spectral analysis of
non-stationary
spatial processes
that is based on the concept of spatial spectra, i.e.
spectral functions which are space-dependent.
This notion of spatial spectra
generalizes the definition of spectra
for stationary processes, and under certain conditions, the spatial
spectrum at each location can be estimated from a single realization of the
spatial process.
The motivation for this work is the modeling and prediction
of ozone
concentrations over different geo-political boundaries
for assessment of compliance with ambient air quality standards.
Keywords:
Bayesian inference; Clean Air Act; Fourier transform; Matern
covariance; kriging; periodogram; spatial statistics; variogram
Downloads:
Data and Software available from
http://www.stat.ncsu.edu/~fuentes/fourthmax.dat
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