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Bevilacqua, M., Caamano-Carrillo, C., Arellano-Valle, R. B., & Gomez, C. (2022). A class of random fields with two-piece marginal distributions for modeling point-referenced data with spatial outliers. Test, 31(3), 644–674.
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.
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Blasi, F., Caamano-Carrillo, C., Bevilacqua, M., & Furrer, R. (2022). A selective view of climatological data and likelihood estimation. Spat. Stat., 50(SI), 100596.
Abstract: This article gives a narrative overview of what constitutes climatological data and their typical features, with a focus on aspects relevant to statistical modeling. We restrict the discussion to univariate spatial fields and focus on maximum likelihood estimation. To address the problem of enormous datasets, we study three common approximation schemes: tapering, direct misspecification, and composite likelihood for Gaussian and nonGaussian distributions. We focus particularly on the so-called 'sinh-arcsinh distribution', obtained through a specific transformation of the Gaussian distribution. Because it has flexible marginal distributions – possibly skewed and/or heavy-tailed – it has a wide range of applications. One appealing property of the transformation involved is the existence of an explicit inverse transformation that makes likelihood-based methods straightforward. We describe a simulation study illustrating the effects of the different approximation schemes. To the best of our knowledge, a direct comparison of tapering, direct misspecification, and composite likelihood has never been made previously, and we show that direct misspecification is inferior. In some metrics, composite likelihood has a minor advantage over tapering. We use the estimation approaches to model a high-resolution global climate change field. All simulation code is available as a Docker container and is thus fully reproducible. Additionally, the present article describes where and how to get various climate datasets. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license
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Morales-Onate, V., Crudu, F., & Bevilacqua, M. (2021). Blockwise Euclidean likelihood for spatio-temporal covariance models. Econ. Stat., 20, 176–201.
Abstract: A spatio-temporal blockwise Euclidean likelihood method for the estimation of covariance models when dealing with large spatio-temporal Gaussian data is proposed. The method uses moment conditions coming from the score of the pairwise composite likelihood. The blockwise approach guarantees considerable computational improvements over the standard pairwise composite likelihood method. In order to further speed up computation, a general purpose graphics processing unit implementation using OpenCL is implemented. The asymptotic properties of the proposed estimator are derived and the finite sample properties of this methodology by means of a simulation study highlighting the computational gains of the OpenCL graphics processing unit implementation. Finally, there is an application of the estimation method to a wind component data set. (C) 2021 EcoSta Econometrics and Statistics. Published by Elsevier B.V. All rights reserved.
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