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

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...

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Bibliographic Details
Published in:Test (Madrid, Spain) Spain), 2022-09, Vol.31 (3), p.644-674
Main Authors: Bevilacqua, Moreno, Caamaño-Carrillo, Christian, Arellano-Valle, Reinaldo B., Gómez, Camilo
Format: Article
Language:English
Subjects:
Bivariate analysis
Economics
Fields (mathematics)
Finance
Insurance
Management
Mathematical analysis
Mathematics and Statistics
Modelling
Original Paper
Outliers (statistics)
Spatial data
Statistical Theory and Methods
Statistics
Statistics for Business
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Summary: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.
ISSN:1133-0686
1863-8260
DOI:10.1007/s11749-021-00797-5