Mittag-Leffler vector random fields with Mittag-Leffler direct and cross covariance functions

Ma, Chunsheng

doi:10.1007/s10463-013-0398-9

Cited by 11 publications

(7 citation statements)

References 33 publications

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“…There is thus a need for multivariate random fields that are more general than the Gaussian random field. Examples of such models in the literature are multivariate max‐stable processes for spatial extremes (Genton et al ., ) and Mittag‐Leffler random fields (Ma, ). A common approach for constructing non‐Gaussian fields is to multiply a Gaussian random field with a random scalar.…”

Section: Introductionmentioning

confidence: 99%

Multivariate Type G Matérn Stochastic Partial Differential Equation Random Fields

Bolin

Wallin

2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary For many applications with multivariate data, random‐field models capturing departures from Gaussianity within realizations are appropriate. For this reason, we formulate a new class of multivariate non‐Gaussian models based on systems of stochastic partial differential equations with additive type G noise whose marginal covariance functions are of Matérn type. We consider four increasingly flexible constructions of the noise, where the first two are similar to existing copula‐based models. In contrast with these, the last two constructions can model non‐Gaussian spatial data without replicates. Computationally efficient methods for likelihood‐based parameter estimation and probabilistic prediction are proposed, and the flexibility of the models suggested is illustrated by numerical examples and two statistical applications.

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Section: Introductionmentioning

confidence: 99%

Multivariate Type G Matérn Stochastic Partial Differential Equation Random Fields

Bolin

Wallin

2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…The Gaussian assumption makes a spatial model simple in structure and facilitates statistical predictions, but this assumption is often not supported by the data. To deal with this issue, we may consider non-Gaussian processes (Du et al, 2012, Ma, 2013a, 2013b, 2015, Du, Ma and Li, 2013), such as the skew-Gaussian (Alegría et al, 2017a) and the Tukey gand-h random fields (Xu and Genton, 2017). These are promising for various applications, but their implementation remains unexplored.…”

Section: Discussionmentioning

confidence: 99%

Spherical Process Models for Global Spatial Statistics

2017

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Abstract. Statistical models used in geophysical, environmental, and climate science applications must reflect the curvature of the spatial domain in global data. Over the past few decades, statisticians have developed covariance models that capture the spatial and temporal behavior of these global data sets. Though the geodesic distance is the most natural metric for measuring distance on the surface of a sphere, mathematical limitations have compelled statisticians to use the chordal distance to compute the covariance matrix in many applications instead, which may cause physically unrealistic distortions. Therefore, covariance functions directly defined on a sphere using the geodesic distance are needed. We discuss the issues that arise when dealing with spherical data sets on a global scale and provide references to recent literature. We review the current approaches to building process models on spheres, including the differential operator, the stochastic partial differential equation, the kernel convolution, and the deformation approaches. We illustrate realizations obtained from Gaussian processes with different covariance structures and the use of isotropic and nonstationary covariance models through deformations and geographical indicators for global surface temperature data. To assess the suitability of each method, we compare their log-likelihood values and prediction scores, and we end with a discussion of related research problems.

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“…form a covariance matrix function, as is shown in the proof of Theorem 4, Ma (2013). Using identities (3) and (13), we rewrite (11) as…”

Section: Proof Of Theoremmentioning

confidence: 99%

Logistic vector random fields with logistic direct and cross covariances

Balakrishnan

Wang

2015

Journal of Statistical Planning and Inference

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Elliptically contoured random field Gaussian random field Isotropic Logistic distribution Spherically invariant random field Stationary Variogram a b s t r a c tThe logistic vector random field is introduced in this paper as a scale mixture of Gaussian vector random fields, and is thus a particular elliptically contoured (spherically invariant) vector random field. Such a logistic vector random field is characterized by its mean function and covariance matrix function just as in the case of Gaussian vector random fields, and so it is flexible enough to allow for any possible mean structure or covariance matrix structure. We also derive covariance matrix functions whose direct and cross covariances are of the logistic type.

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Mittag-Leffler vector random fields with Mittag-Leffler direct and cross covariance functions

Cited by 11 publications

References 33 publications

Multivariate Type G Matérn Stochastic Partial Differential Equation Random Fields

Multivariate Type G Matérn Stochastic Partial Differential Equation Random Fields

Spherical Process Models for Global Spatial Statistics

Logistic vector random fields with logistic direct and cross covariances

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