Non-Gaussian geostatistical modeling using (skew) t processes

Moreno Bevilacqua, Christian Caamaño-Carrillo, Reinaldo B. Arellano-Valle, Víctor Morales-Oñate

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

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 t 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) t process, we study the second-order and geometrical properties and in the t 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 t process. Moreover we compare the performance of the optimal linear predictor of the t process versus the optimal Gaussian predictor. Finally, the effectiveness of our methodology is illustrated by analyzing a georeferenced dataset on maximum temperatures in Australia.

Original languageEnglish
Pages (from-to)212-245
Number of pages34
JournalScandinavian Journal of Statistics
Volume48
Issue number1
DOIs
StatePublished - Mar 2021

Keywords

  • Gaussian scale mixture
  • heavy-tailed processes
  • hypergeometric functions
  • multivariate skew-normal distribution
  • pairwise likelihood

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