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Non-Gaussian Geostatistical Modeling using (skew) t Processes
We propose a new model for regression and dependence analysis when addressing
spatial data with possibly heavy tails and an asymmetric marginal distribution.
We first propose a stationary process with marginals obtained through scale
mixing of a Gaussian process with an inverse square root process with Gamma
marginals. We then generalize this construction by considering a skew-Gaussian
process, thus obtaining a process with skew-t marginal distributions. For the
proposed (skew) process we study the second-order and geometrical
properties and in the case, we provide analytic expressions for the
bivariate distribution. In an extensive simulation study, we investigate the
use of the weighted pairwise likelihood as a method of estimation for the
process. Moreover we compare the performance of the optimal linear predictor of
the process versus the optimal Gaussian predictor. Finally, the
effectiveness of our methodology is illustrated by analyzing a georeferenced
dataset on maximum temperatures in Australi
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