Analogies and correspondences between variograms and covariance functions

By Tilmann Gneiting, Zoltán Sasvári, Martin Schlather. 2001

75 citations recorded by the source corpus.

Subfields: Environmental Engineering, Finance

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Citations in the corpus

Variogram or semivariogram? Understanding the variances in a variogram (2008, background): “Some authors call the function c a ‘variogram’ (Wackernagel 2003; Worboys 1995; Gneiting et al. 2001), several authors call it a ‘semivariogram’ (Journel and Huijbregts 1978; Cressie 1991; Goovaerts 1997; Burrough and McDonnell 1998; Olea 1999; Stein 1999; Gringarten and Deutsch 2001), stating tha”
Modeling Nonstationary Processes Through Dimension Expansion (2010, unknown): “It is worth noting that while we have developed the spatial model in terms of variograms, it could alternatively be expressed in terms of covariances; see, for example, Gneiting et al. (2001) for a thorough comparison of the two approaches.”
Some covariance models based on normal scale mixtures (2011, unknown): “Schoenberg’s (1938b) theorem states that a function γ̃ :Rd → R with γ̃(0) = 0 is a variogram if and only if exp(−rγ̃) is a covariance function for all r > 0, see also Gneiting et al. (2001).”
Geostatistical Space-Time Models, Stationarity, Separability, and Full Symmetry (2007, unknown): “A convenient choice is an isotropic model, CS(h) = c0(khk), h 2 d , wherec0 is one of the standard models in geostatistics, such as the powered exponential class (see, for instance, Diggle, Tawn and Moyeed 1998), the Whittle-Mat ern class (Whittle 1954; Mat ern 1986) and the Cauchy class ( Gneiting ”
Statistical Modelling of Spatial Extremes (2012, background): “Gneiting et al. (2001) discuss the relationships between semivariograms and covariance functions: in particular, a real function on R2 satisfying γ(0) = 0 is the semivariogram of an intrinsically stationary process if and only if it is conditionally negative definite, i.e., n ∑ i,j=1 aiajγ(xi − xj)…”
Detecting dependence between marks and locations of marked point processes (2004, background): “….4/ Condition (c) of theorem 1, concerning the conditional negative definiteness of the mark variogram, is difficult to check directly, although several necessary and sufficient conditions are known; see Gneiting et al. (2001) and Sasvári (1994) for overviews over properties of the variogram.”