Multivariate Spatial Prediction in the Presence of Non-Linear Trend and Covariance Non-Stationarity

Abstract

SUMMARYWhen two or more spatial processes are punctually observed over a region, a multivariate predictor can account for spatial cross-covariance among the variables and thus potentially yield more reliable predictions and lower estimated prediction standard errors. If the spatial processes exhibit first-and/or second-order non-stationarity, however, standard cokriging-based predictors may not be adequate. A new cokrigingbased multivariate predictor is presented capable of modelling non-linear trend, non-stationary spatial covariance, and the case where the covariable also enters as a covariate. This method is used to predict 1991 sulphate deposition over the conterminous US with the aid of the more spatially dense National Weather Service precipitation data. It is found that there are only small differences between sulphate predictions and estimated prediction standard errors and those computed under enforced zero cross-covariance. Failing to include the covariate effect of precipitation, however, results in non-negligible differences in such predictions and prediction standard error estimates.

Multivariate Spatial Outlier Detection Using Robust Geographically Weighted Methods

“…Here, a true robust calibration would need to account for an (initially) unknown set of outliers when: (A) fitting its covariance functions (see Lark 2002) and (B) predicting, say using Winsorised data (see Hawkins and Cressie 1984). A further refinement could replace the globally-defined matrix covariance function with a local version (see Haas 1996).…”

Modelling hedonic residential rents for land use and transport simulation while considering spatial effects

“…Some of the most popular approaches are the spatially adaptive ltering methods (Trigg and Leach 1967;Widrow and Hoff 1960), expansion methods  (Fotheringham and Pitts 1995), multi-level approaches (Goldstein 1987;Jones 1991), spatial simultaneous autoregressive approaches such as spatial lag and spatial error models (Anselin 1988), as well as geographically weighted regression (GWR) models (Fotheringham et al 2002). Beyond that, there are, for example, the local kriging and co-kriging methodology of Haas (1995Haas ( , 1996 and the Bayesian spatially varying coefficient process models of Gelfand et al (2003). Each of these approaches has its bene ts and drawbacks, but all emphasize that parameters identi ed in global models may not resemble parameters estimated in local models.…”

Spatial Modeling of Butterfly Species Richness Using Tiger Beetles (Cicindelidae) as a Bioindicator Taxon

“…1 (and correspondingly Eq. 8) is a specific example of the more general model associated with universal kriging and a zero-mean, second-order stationary random process, ␦(·) (Cressie 1991, Gotway and Hartford 1996, Haas 1996. The more general model is…”