2018/12/15 by Moreno Bevilacqua, C. Caamaño, Bevilacqua, M. +5
Decision Sciences · Environmental Science · Mathematics · #Advanced Statistical Methods and Models #FOS: Mathematics #Optimal Experimental Design Methods #Soil Geostatistics and Mapping #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1812.06310
openalex publication_date 2018/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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