Tukey<i>g</i>-and-<i>h</i>Random Fields

Xu, Ganggang; Genton, Marc G.

doi:10.1080/01621459.2016.1205501

Cited by 100 publications

(95 citation statements)

References 43 publications

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“…On the other hand, wrapped-Gaussian RFs have been introduced in the literature for modeling directional spatial data, arising in the study of wave and wind directions (see Jona-Lasinio et al, 2012). In addition, Xu and Genton (2016a) propose a flexible class of fields named the Tukey g-and-h RFs.…”

Section: Introductionmentioning

confidence: 99%

Estimating covariance functions of multivariate skew-Gaussian random fields on the sphere

et al. 2017

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This paper considers a multivariate spatial random field, with each component having univariate marginal distributions of the skew-Gaussian type. We assume that the field is defined spatially on the unit sphere embedded in R 3 , allowing for modeling data available over large portions of planet Earth. This model admits explicit expressions for the marginal and cross covariances. However, the n-dimensional distributions of the field are difficult to evaluate, because it requires the sum of 2 n terms involving the cumulative and probability density functions of a n-dimensional Gaussian distribution. Since in this case inference based on the full likelihood is computationally unfeasible, we propose a composite likelihood approach based on pairs of spatial observations. This last being possible thanks to the fact that we have a closed form expression for the bivariate distribution. We illustrate the effectiveness of the method through simulation experiments and the analysis of a real data set of minimum and maximum surface air temperatures.

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Section: Introductionmentioning

confidence: 99%

Estimating covariance functions of multivariate skew-Gaussian random fields on the sphere

et al. 2017

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“…Unfortunately, we could not derive such an expression for the time-changed models (see discussion of Theorem 1 in the Appendix). Note that such an expression is available for TG models when a specific marginal transformation such as the Tuckey transformation is used (see Xu & Genton, 2017) but not for general TG models. located near the shore where the waves are asymmetric.…”

Section: Up-down Asymmetries: Atmospheric Pressure Datamentioning

confidence: 99%

Time‐change models for asymmetric processes

Ailliot

Delyon

Monbet

et al. 2019

Scandinavian J Statistics

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Many records in environmental sciences exhibit asymmetric trajectories. The physical mechanisms behind these records may lead for example to sample paths with different characteristics at high and low levels (up–down asymmetries) or in the ascending and descending phases leading to time irreversibility (front–back asymmetries). Such features are important for many applications, and there is a need for simple and tractable models that can reproduce them. In this paper, we explore original time‐change models where the clock is a stochastic process that depends on the observed trajectory. The ergodicity of the proposed model is established under general conditions, and this result is used to develop nonparametric estimation procedures based on the joint distribution of the process and its derivative. The methodology is illustrated on meteorological and oceanographic data sets. We show that, combined with a marginal transformation, the proposed methodology is able to reproduce important characteristics of the data set such as marginal distributions, up‐crossing intensity, and up–down and front–back asymmetries.

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“…Commonly used transformations include lognormal (De Oliveira, ), square‐root (Johns, Nychka, Kittel, & Daly, ), Box–Cox (De Oliveira, Kedem, & Short, ), and power transformations (Allcroft & Glasbey, ). Recently, a new family of trans‐Gaussian random fields, the TGH random field, was proposed by Xu and Genton (). The TGH random fields accommodate different levels of skewness and tail heaviness in marginal distributions.…”

Section: Tgh Random Fields With Matérn Covariancementioning

confidence: 99%

“…Then, the ML estimator (MLE),̂, of is computed by maximizing l( ), which is equivalent to solving l( ) i = 0, for i = 1, … , p. We are interested in the performance of the parameter estimation for the covariance model and prediction at unknown locations based on the Gaussian likelihood when the true underlying random field is non-Gaussian. We focus our attention on one flexible class of trans-Gaussian random fields proposed by Xu and Genton (2017), the Tukey g-and-h (TGH) random field, in which g ∈ R controls skewness and h ≥ 0 controls tail heaviness.…”

Section: Introductionmentioning

confidence: 99%

Gaussian likelihood inference on data from trans‐Gaussian random fields with Matérn covariance function

Yuan

Genton

2017

Environmetrics

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Gaussian likelihood inference has been studied and used extensively in both statistical theory and applications due to its simplicity. However, in practice, the assumption of Gaussianity is rarely met in the analysis of spatial data. In this paper, we study the effect of non‐Gaussianity on Gaussian likelihood inference for the parameters of the Matérn covariance model. By using Monte Carlo simulations, we generate spatial data from a Tukey g‐and‐h random field, a flexible trans‐Gaussian random field, with the Matérn covariance function, where g controls skewness and h controls tail heaviness. We use maximum likelihood based on the multivariate Gaussian distribution to estimate the parameters of the Matérn covariance function. We illustrate the effects of non‐Gaussianity of the data on the estimated covariance function by means of functional boxplots. Thanks to our tailored simulation design, a comparison of the maximum likelihood estimator under both the increasing and fixed domain asymptotics for spatial data is performed. We find that the maximum likelihood estimator based on Gaussian likelihood is overall satisfying and preferable than the non‐distribution‐based weighted least squares estimator for data from the Tukey g‐and‐h random field. We also present the result for Gaussian kriging based on Matérn covariance estimates with data from the Tukey g‐and‐h random field and observe an overall satisfactory performance.

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Tukeyg-and-hRandom Fields

Cited by 100 publications

References 43 publications

Estimating covariance functions of multivariate skew-Gaussian random fields on the sphere

Estimating covariance functions of multivariate skew-Gaussian random fields on the sphere

Time‐change models for asymmetric processes

Gaussian likelihood inference on data from trans‐Gaussian random fields with Matérn covariance function

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