A class of random fields with two-piece marginal distributions for modeling point-referenced data with spatial outliers

• Moreno Bevilacqua ^[1] ; Christian Caamaño-Carrillo ^[2] ; Reinaldo B. Arellano-Valle ; Camilo Gómez ^[3]
  1. [1] Universidad Adolfo Ibáñez

     Universidad Adolfo Ibáñez

     Santiago, Chile

     
  2. [2] Universidad del Bío-Bío

     Universidad del Bío-Bío

     Comuna de Concepción, Chile

     
  3. [3] Departamento de Estadística, Universidad of Valparaíso, Gran Bretaña 1091, Valparaíso, Chile

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• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 31, Nº. 3, 2022, págs. 644-674
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this paper, we propose a new class of non-Gaussian random fields named two-piece random fields. The proposed class allows to generate random fields that have flexible marginal distributions, possibly skewed and/or heavy-tailed and, as a consequence, has a wide range of applications. We study the second-order properties of this class and provide analytical expressions for the bivariate distribution and the associated correlation functions. We exemplify our general construction by studying two examples: two-piece Gaussian and two-piece Tukey-h random fields. An interesting feature of the proposed class is that it offers a specific type of dependence that can be useful when modeling data displaying spatial outliers, a property that has been somewhat ignored from modeling viewpoint in the literature for spatial point referenced data. Since the likelihood function involves analytically intractable integrals, we adopt the weighted pairwise likelihood as a method of estimation. The effectiveness of our methodology is illustrated with simulation experiments as well as with the analysis of a georeferenced dataset of mean temperatures in Middle East.