Publicación: NON-GAUSSIAN GEOSTATISTICAL MODELING USING (SKEW) T PROCESSES
Fecha
2021
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SCANDINAVIAN JOURNAL OF STATISTICS
Resumen
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.
