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Abstract:
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For analyzing multivariate geostatistical spatial data, there arises the need for flexible explanatory stochastic models. Here, we propose a general constructive approach for building suitable models based on convolution of covariance functions. We begin with a general theorem that asserts under weak conditions, cross convolution of covariance functions provides a valid cross-covariance function. We also obtain a result on dependence induced by such convolution. Because, in general, convolution does not provide closed-form integration, we discuss efficient computation. We then suggest introducing such specification through a Gaussian process to model multivariate spatial random effects within a hierarchical model. We note that modeling spatial random effects in this way is parsimonious relative to, say, the linear model of coregionalization.
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