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intamap (version 1.3-21)

copulaEstimation: ML-estimation of the spatial copula model parameters

Description

Estimates parameters of the spatial copula model using maximum likelihood.

Usage

copulaEstimation(obj,margin,trend,correlation,anisotropy,copula,tol=0.001,...)

Arguments

obj
Intamap object, see description in intamap-package
margin
list with the following elements: [object Object],[object Object],[object Object],[object Object]
trend
list with the following elements: [object Object],[object Object],[object Object],[object Object]
correlation
list with the following elements: [object Object],[object Object],[object Object],[object Object]
anisotropy
list with the following elements: [object Object],[object Object],[object Object]
copula
list with the following elements: [object Object],[object Object],[object Object],[object Object]
tol
Tolerance level for the optimization process.
...
Arguments to be passed to optim.

Value

  • A list with the following elements:
  • marginSame as the input except that the list element "params" now consists of the optimized parameters of the marginal distribution function.
  • trendSame as the input except that the list element "params" now consists of the optimized parameters of the trend model.
  • correlationSame as the input except that the list element "params" now consists of the optimized parameters of the correlation function model.
  • anisotropySame as the input except that the list element "params" now consists of the optimized parameters of geometric anisotropy.
  • copulaSame as the input except that the list element "params" now consists of the optimized copula parameters.

Details

copulaEstimation performs maximum likelihood estimation of all possible parameters included in the Gaussian and chi-squared spatial copula model: parameters of the predefined family of marginal distributions (including spatial trend or external drift), correlation function parameters, parameters for geometric anisotropy and parameters for the copula (only used for the chi-squared copula model). Due to the large number of variables that need to be optimized, a profile-likelihood approach is used. Although convergence to a global optimum is not assured, the profile-likelihood method makes it less likely that the optimization routine, optim, gets stuck in a local optimum. The result of copulaEstimation is a list containing all parameter point estimates that are needed for plug-in spatial prediction. It is advisable to check the output of the algorithm by trying different starting values for the optimization.

References

Kazianka, H. and Pilz, J. (2009), Spatial Interpolation Using Copula-Based Geostatistical Models. GeoENV2008 - Geostatistics for Environmental Application (P. Atkinson, C. Lloyd, eds.), Springer, New York

See Also

bayesCopula, spatialPredict, estimateParameters

Examples

Run this code
data(intamapExampleObject)
## estimate parameters for the copula model

copula<-list(method="norm")
anisotropy<-list(lower=c(0,1),upper=c(pi,Inf),params=c(pi/3,2))
correlation<-list(model="Ste",lower=c(0.01,0.01,0.01),upper=c(0.99,Inf,20),params=c(0.05,4,3))
margin<-list(name="gev",lower=c(0.01,-Inf),upper=c(Inf,Inf),params=c(30,0.5))
trend<-list(F=as.matrix(rep(1,196)),lower=-Inf,upper=Inf,params=40)
estimates<-copulaEstimation(intamapExampleObject,margin,trend,correlation,anisotropy,copula)
## make predictions at unobserved locations
predictions<-bayescopula(intamapExampleObject,estimates,search=25,calc=list(mean=TRUE,variance=TRUE,excprob=40,quantile=0.95))

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