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A class of covariate-dependent spatiotemporal covariance functions for the analysis of daily ozone concentration. (English) Zbl 1234.62125

Summary: In geostatistics, it is common to model spatially distributed phenomena through an underlying stationary and isotropic spatial process. However, these assumptions are often untenable in practice because of the influence of local effects in the correlation structure. Therefore, it has been of prolonged interest in the literature to provide flexible and effective ways to model nonstationarity in the spatial effects. Arguably, due to the local nature of the problem, we might envision that the correlation structure would be highly dependent on local characteristics of the domain of study, namely, the latitude, longitude and altitude of the observation sites, as well as other locally defined covariate information. We provide a flexible and computationally feasible way for allowing the correlation structure of the underlying processes to depend on local covariate information. We discuss the properties of the induced covariance functions and methods to assess its dependence on local covariate information. The proposed method is used to analyze daily ozone in the southeast United States.

MSC:

62M30 Inference from spatial processes
62P12 Applications of statistics to environmental and related topics
86A32 Geostatistics
65C60 Computational problems in statistics (MSC2010)
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