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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Moreno Bevilacqua & Christian Caamaño-Carrillo & Reinaldo B. Arellano-Valle & Camilo Gómez, 2022. "A class of random fields with two-piece marginal distributions for modeling point-referenced data with spatial outliers," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 644-674, September.
    • Handle: RePEc:spr:testjl:v:31:y:2022:i:3:d:10.1007_s11749-021-00797-5
    DOI: 10.1007/s11749-021-00797-5
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    References listed on IDEAS

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    1. Caamaño-Carrillo, Christian & Bevilacqua, Moreno & López, Cristian & Morales-Oñate, Víctor, 2024. "Nearest neighbors weighted composite likelihood based on pairs for (non-)Gaussian massive spatial data with an application to Tukey-hh random fields estimation," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).

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