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Multiresolution models for nonstationary spatial covariance functions

Geophysical Statistics Project, National Center for Atmospheric Research, Boulder, CO, USA, nychka{at}ucar.edu

Christopher Wikle

Department of Statistics, University of Missouri, Columbia, MO, USA

J Andrew Royle

US Fish and Wildlife Service Adaptive Management and Assessment Team, Laurel, MD, USA

Many geophysical and environmental problems depend on estimating a spatial process that has nonstationary structure. A nonstationary model is proposed based on the spatial field being a linear combination of multiresolution (wavelet) basis functions and random coefficients. The key is to allow for a limited number of correlations among coefficients and also to use a wavelet basis that is smooth. When approximately 6% nonzero correlations are enforced, this representation gives a good approximation to a family of Matern covariance functions. This sparseness is important not only for model parsimony but also has implications for the efficient analysis of large spatial data sets. The covariance model is successfully applied to ozone model output and results in a nonstationary but smooth estimate.

Key Words: wavelet • Kriging • multiresolution • ozone pollution

Statistical Modelling, Vol. 2, No. 4, 315-331 (2002)
DOI: 10.1191/1471082x02st037oa


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