A formal test for nonstationarity of spatial stochastic processes

Fuentes, Montserrat

doi:10.1016/j.jmva.2004.09.003

Cited by 68 publications

(53 citation statements)

References 27 publications

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“…We call C the space-time covariance function of the process, and its restrictions C(·, 0) and C(0, ·) are purely spatial and purely temporal covariance functions, respectively. For tests of stationarity we point to Fuentes (2005b) and references therein.…”

Section: Introductionmentioning

confidence: 99%

Geostatistical Space-Time Models, Stationarity, Separability, and Full Symmetry

Gneiting¹,

Genton²,

Guttorp³

2006

C&H/CRC Monographs on Statistics &Amp; Applied Probability

208

282

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Geostatistical approaches to modeling spatio-temporal data rely on parametric covariance models and rather stringent assumptions, such as stationarity, separability and full symmetry. This paper reviews recent advances in the literature on space-time covariance functions in light of the aforementioned notions, which are illustrated using wind data from Ireland. Experiments with time-forward kriging predictors suggest that the use of more complex and more realistic covariance models results in improved predictive performance.

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Section: Introductionmentioning

confidence: 99%

Geostatistical Space-Time Models, Stationarity, Separability, and Full Symmetry

Gneiting¹,

Genton²,

Guttorp³

2006

C&H/CRC Monographs on Statistics &Amp; Applied Probability

208

282

View full text Add to dashboard Cite

show abstract

“…The assumption of Gaussian data lies at the heart of many spatial analyses (Gelfand and Schliep 2016) and is easily checked with a QQ plot. The assumption of weak stationarity may be questionable for spatial data over large geographic regions and methods have been developed for testing this assumption (see, e.g., Corstanje, Grunwald, and Lark 2008;Fuentes 2005;Jun and Genton 2012;Bandyopadhyay and Subba Rao 2017). The second assumption required is a mixing condition that states that the dependence between observations goes to 0 at large distances (Hall and Patil 1994;Sherman and Carlstein 1994).…”

Section: Discussionmentioning

confidence: 99%

spTest: An R Package Implementing Nonparametric Tests of Isotropy

Weller¹

2018

J. Stat. Soft.

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An important step in modeling spatially-referenced data is appropriately specifying the second order properties of the random field. A scientist developing a model for spatial data has a number of options regarding the nature of the dependence between observations. One of these options is deciding whether or not the dependence between observations depends on direction, or, in other words, whether or not the spatial covariance function is isotropic. Isotropy implies that spatial dependence is a function of only the distance and not the direction of the spatial separation between sampling locations. A researcher may use graphical techniques, such as directional sample semivariograms, to determine whether an assumption of isotropy holds. These graphical diagnostics can be difficult to assess, subject to personal interpretation, and potentially misleading as they typically do not include a measure of uncertainty. In order to escape these issues, a hypothesis test of the assumption of isotropy may be more desirable. To avoid specification of the covariance function, a number of nonparametric tests of isotropy have been developed using both the spatial and spectral representations of random fields. Several of these nonparametric tests are implemented in the R package spTest, available on CRAN. We demonstrate how graphical techniques and the hypothesis tests programmed in package spTest can be used in practice to assess isotropy properties.

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“…These simulations are omitted from this paper. When calculating the spectral density function of the Matérn covariance function, we must consider the aliasing phenomenon (Fuentes (2005)) because the observations exist on an integer lattice. Tables 1-3 show that as N increases, the empirical variance multiplied by D 2 N 2 goes to the asymptotic variance in all cases, as in Theorem 2.…”

Section: Computational Experimentsmentioning

confidence: 99%

Pseudo Best Estimator by a Separable Approximation of Spatial Covariance Structures

Hirano

2014

JJSS

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We consider a linear regression model with a spatially correlated error term on a lattice. When estimating coefficients in the linear regression model, the generalized least squares estimator (GLSE) is used if the covariance structures are known. However, the GLSE for large spatial data sets is computationally expensive because of the matrix inversion. To reduce the computational complexity, we propose a pseudo best estimator (PBE) using spatial covariance structures approximated by separable covariance functions and derive its asymptotic covariance matrix. Monte Carlo simulations demonstrate that our proposed PBE performs well.

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A formal test for nonstationarity of spatial stochastic processes

Cited by 68 publications

References 27 publications

Geostatistical Space-Time Models, Stationarity, Separability, and Full Symmetry

Geostatistical Space-Time Models, Stationarity, Separability, and Full Symmetry

spTest: An R Package Implementing Nonparametric Tests of Isotropy

Pseudo Best Estimator by a Separable Approximation of Spatial Covariance Structures

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