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

Moreno Bevilacqua (), Christian Caamaño-Carrillo, Reinaldo B. Arellano-Valle and Camilo Gómez
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Moreno Bevilacqua: Universidad Adolfo Ibáñez
Christian Caamaño-Carrillo: Universidad del Bío-Bío
Reinaldo B. Arellano-Valle: Pontificia Universidad Católica de Chile
Camilo Gómez: Universidad of Valparaíso

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2022, vol. 31, issue 3, No 4, 644-674

Abstract: Abstract 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.

Keywords: Asymmetric random fields; Composite likelihood; Spatial outliers; Tukey-h distribution; 60G15; 62H11; 62F10 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11749-021-00797-5

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