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Abstract:
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The growing attention to the importance of data, paired with increasingly advanced data collection technology, has brought challenges to statisticians from all areas, including spatial statistics. On one hand, the sheer volume of data posts substantial computational burden; on the other hand, data may come from different sources which demands multivariate spatial modeling to provide thorough insight into the underlying spatial processes. Building multivariate spatial models requires keeping a subtle balance between the model complexity and flexibility. The former involves manipulating the parameter structure to create a valid multivariate covariance function and the latter involves taking advantage of the choices among a large selection of available univariate spatial models to fit the data.
Hu and Zhang propose a univariate modeling approach which uses Karhunen-Loeve transformation to provide significant data reduction and offers great relief for computation. It has the ability to approximate any given covariance function with a selected set of basis functions. By incorporating this approach into the semi-parametric approach to multivariate spatial modeling by Wang and Zhang, w
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