Classes of compactly supported covariance functions for multivariate random fields

Daley, D. J.; Porcu, Emilio; Bevilacqua, Moreno

doi:10.1007/s00477-014-0996-y

Cited by 56 publications

(59 citation statements)

References 29 publications

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“…Another example of model can be found in Daley et al. (), where R ( h ;.) is a compactly supported correlation model of the Wendland type (Wendland, ):

R (bold-italich; bold-italicψ) = ((), 1 + (ν + 1) \frac{bold-italich}{β}) {((), 1 - \frac{bold-italich}{β})}_{+}^{ν + 1}

with β > 0 and

ν > \frac{(d + 1)}{2} + 2

.…”

Section: Parametric Bivariate Covariance Modelsmentioning

confidence: 99%

“…The authors find necessary and sufficient conditions on the colocated correlation parameter 12 in order that model (4) to be valid. Another example of model (4) can be found in Daley et al (2015), where R.hI :/ is a compactly supported correlation model of the Wendland type (Wendland, 1995):…”

Section: Parametric Bivariate Covariance Modelsmentioning

confidence: 99%

“…To overcome these drawbacks, new and more flexible models have been proposed in recent years (see Genton and Kleiber, 2015, for an excellent review). For example, Gneiting et al (2010) and Apanasovich et al (2012) introduced the bivariate Matérn model, and Daley et al (2015) proposed a bivariate model with a compactly supported correlation function of the Wendland type (Wendland, 1995). The models proposed by the previous authors share a common general construction for a bivariate parametric model, which consists of modeling the marginal and the cross-covariance functions using a specific univariate covariance model with possibly different parameters, while the marginal correlation between the components is described using the so-called colocated correlation parameter (Gneiting et al, 2010).…”

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confidence: 99%

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Assessing the significance of the correlation between the components of a bivariate Gaussian random field

2015

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Assessing the significance of the correlation between the components of a bivariate random field is of great interest in the analysis of spatial data. This problem has been addressed in the literature using suitable hypothesis testing procedures or using coefficients of spatial association between two sequences. In this paper, testing the association between autocorrelated variables is addressed for the components of a bivariate Gaussian random field using the asymptotic distribution of the maximum likelihood estimator of a specific parametric class of bivariate covariance models. Explicit expressions for the Fisher information matrix are given for a separable and a nonseparable version of the parametric class, leading to an asymptotic test. The empirical evidence supports our proposal, and as a result, in most of the cases, the new test performs better than the modified t test even when the bivariate covariance model is misspecified or the distribution of the bivariate random field is not Gaussian. Finally, to illustrate how the proposed test works in practice, we study a real dataset concerning the relationship between arsenic and lead from a contaminated area in Utah, USA.

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“…Another example of model can be found in Daley et al. (), where R ( h ;.) is a compactly supported correlation model of the Wendland type (Wendland, ):

R (bold-italich; bold-italicψ) = ((), 1 + (ν + 1) \frac{bold-italich}{β}) {((), 1 - \frac{bold-italich}{β})}_{+}^{ν + 1}

with β > 0 and

ν > \frac{(d + 1)}{2} + 2

.…”

Section: Parametric Bivariate Covariance Modelsmentioning

confidence: 99%

Section: Parametric Bivariate Covariance Modelsmentioning

confidence: 99%

mentioning

confidence: 99%

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Assessing the significance of the correlation between the components of a bivariate Gaussian random field

2015

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“…Kleiber and Porcu (2015) provided a nonstationary extension of this model, while Porcu et al (2013) considered similar ideas for Buhmann functions and B-splines. Daley, Porcu and Bevilacqua (2015) obtained multivariate Askey functions with different compact supports b ij and the multivariate analogue of Wendland functions. The latter provide a tool for tapering cross-covariance functions such as the multivariate Matérn.…”

Section: Compactly Supported Cross-covariance Functionsmentioning

confidence: 99%

Cross-Covariance Functions for Multivariate Geostatistics

Genton¹,

Kleiber²

2015

Statist. Sci.

259

211

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Continuously indexed datasets with multiple variables have become ubiquitous in the geophysical, ecological, environmental and climate sciences, and pose substantial analysis challenges to scientists and statisticians. For many years, scientists developed models that aimed at capturing the spatial behavior for an individual process; only within the last few decades has it become commonplace to model multiple processes jointly. The key difficulty is in specifying the cross-covariance function, that is, the function responsible for the relationship between distinct variables. Indeed, these cross-covariance functions must be chosen to be consistent with marginal covariance functions in such a way that the second-order structure always yields a nonnegative definite covariance matrix. We review the main approaches to building cross-covariance models, including the linear model of coregionalization, convolution methods, the multivariate Mat\'{e}rn and nonstationary and space-time extensions of these among others. We additionally cover specialized constructions, including those designed for asymmetry, compact support and spherical domains, with a review of physics-constrained models. We illustrate select models on a bivariate regional climate model output example for temperature and pressure, along with a bivariate minimum and maximum temperature observational dataset; we compare models by likelihood value as well as via cross-validation co-kriging studies. The article closes with a discussion of unsolved problems.Comment: Published at http://dx.doi.org/10.1214/14-STS487 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

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“…In recent years, multivariate (or vector-valued) Gaussian processes and random fields have become popular in modeling multivariate spatial datasets (see, e.g., [17,36]). Several classes of multivariate spatial models were introduced in [4,13,14,19,26,30,33]. Two of the challenges in multivariate modeling are to specify the cross-dependence structures and to quantify the effect of the crossdependence on the estimation and prediction performance.…”

Section: Introductionmentioning

confidence: 99%

Joint asymptotics for estimating the fractal indices of bivariate Gaussian processes

Zhou

Xiao

2018

Journal of Multivariate Analysis

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Multivariate (or vector-valued) processes are important for modeling multiple variables. The fractal indices of the components of the underlying multivariate process play a key role in characterizing the dependence structures and statistical properties of the multivariate process.In this paper, under the infill asymptotics framework, we establish joint asymptotic results for the increment-based estimators of bivariate fractal indices. Our main results quantitatively describe the effect of the crossdependence structure on the performance of the estimators.

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Classes of compactly supported covariance functions for multivariate random fields

Cited by 56 publications

References 29 publications

Assessing the significance of the correlation between the components of a bivariate Gaussian random field

Assessing the significance of the correlation between the components of a bivariate Gaussian random field

Cross-Covariance Functions for Multivariate Geostatistics

Joint asymptotics for estimating the fractal indices of bivariate Gaussian processes

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