c173_c273_lec8a_s09[1]

# c173_c273_lec8a_s09[1] - University of California Los...

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University of California, Los Angeles Department of Statistics Statistics C173/C273 Instructor: Nicolas Christou Fitting a model variogram to the sample variogram The parameters of the model variogram can be estimated through ordinary or weighted least squares (and the method of maximum likelihood which is not discussed here): a. Method of ordinary least squares (ols): The parameters of the model variogram are estimated by minimizing the following function: min X h (2ˆ γ ( h ) - 2 γ ( h )) 2 b . Method of weighted least squares: 1. The weights are the number of pairs for each lag distance. The parameters of the model variogram are estimated by minimizing the following function: min X h N ( h ) (2ˆ γ ( h ) - 2 γ ( h )) 2 2. Cressie’s weighted least squares. Here the weights are given by N ( h ) γ ( h ) 2 . The param- eters of the model variogram are estimated by minimizing the following function: min X h N ( h ) ˆ γ ( h ) γ ( h ) - 1 ! 2 The geoR library uses the variofit function for the estimation of the parameters of the model variogram as follows: > b <- as.geodata(a) > variogram1 <- variog(b) > fit <- variofit(variogram1, cov.model="name of model variogram ", ini.cov.pars=c(partial sill, range), fix.nugget=TRUE, nugget=value or fix.nugget=FALSE, nugget=value (default is zero), max.dist=value (default is the maximum distance from the variogram calculation: variogram1\$max.dist), wei="equal", "npairs", "cressie" (default is "npairs")) For the initial parameters we can give a range of values for the partial sill and the range. The

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c173_c273_lec8a_s09[1] - University of California Los...

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