Blur‐generated non‐separable space–time models

By P. Brown, G. Roberts, K. Kåresen, Stefano F. Tonellato. 2000

163 citations recorded by the source corpus.

Subfields: Environmental Engineering, Global and Planetary Change, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/21147ca231c8e3a3723a37cb534ee857b30b2cb2

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Citations in the corpus

Statistical methods for regular monitoring data (2005, background): “…other space–time models that have been suggested in recent works such as Christakos (1992, 2000), Jones and Zhang (1997), Cressie and Huang (1999), Brown et al. (2000), de Iaco et al. (2001, 2002, 2003), Gneiting (2002), Hartfield and Gunst (2003), Ma (2003), Kolovos et al. (2004) and Stein…”
Spatio-temporal variograms and covariance models (2005, background): “…and Stoffer (1986)), stochastic partial differential or integral equations (e.g. Whittle (1954), (1962), Heine (1955), Jones and Zhang (1997), Brown et al. (2000), Storvik et al. (2002), and Anh et al. (2003)), the Kalman filter (e.g. Huang and Cressie (1996), Meiring et al. (1998), Wikle…”
Recent developments on the construction of spatio-temporal covariance models (2008, background): “For references see Onof et al. (1996), Cowpertwait (1998), Northrop (1998), Wheater et al. (2000), and Brix and Chadeuf (2002) .”
Geostatistical Space-Time Models, Stationarity, Separability, and Full Symmetry (2007, background): “The celebrated theorem of Bochner (1955) states that a continuous function is positive denite if and only it is the Fourier transform of a nite nonnegative measure.”
A kernel-based spectral model for non-Gaussian spatio-temporal processes (2002, methodology): “Although this can be controlled via the dilation parameter, it is a common (and often desirable) feature of the stochastic IDE model (Brown et al., 2000).”
Testing for separability of spatial–temporal covariance functions (2006, methodology): “For \blur-generated" models, Brown et al. (2000) studied separability using a likelihood approa h.Mit hell (2002), and Mit hell, Genton and Gumpertz (2002) proposed a likelihood ratio test of separabilityfor an i.i.d. multivariate pro ess, this likelihood-based method an be used with…”
Aggregation of Space-Time Processes (2001, background): “1 More recent discussions and applications of the space-time AR model in econometrics are Elhorst (2001) and Szulc (2000), while a generalization of the model to continuous space is proposed by Brown et al. (2000) .”
Space–Time Covariance Functions (2005, methodology): “The model given by Brown et al. (2000) is the special case of (10) when φ(w) = w′u, β(w) = λ + 12 w′ w and F(dw)/dw = exp(− 12 w′ w)/(λ + 12 w′ w) for some λ ≥ 0, a vector u, and positive definite matrix .”
Separable approximations of space‐time covariance matrices (2007, background): “However, another reason is that the covariance function (1) has to be positive definite due to the famed theorem of Bochner (1955) .”