R: Details on fitting Gaussian random fields, including Box-Cox...

fitgauss {RandomFields} | R Documentation

## Details on fitting Gaussian random fields, including Box-Cox transformation

### Description

Here some details of `RFfit` are given concerning the fitting of models for Gaussian random fields

This documentation is far from being complete.

### Maximum likelihood

The application of the usual maximum likelihood method and reporting the result is the default.

### Least squares

The weighted least squares methods minimise

∑_{i} w_i (\hat γ(h_i) - γ(h_i))^2

over all parametrised models of γ. Here, i runs over all N bins of the binned variogram \hat γ and h_i is the centre of bin i.

The following variants of the least squares methods, passed as `sub.methods` in `RFfit` are implemented.

`'self'`

  w_i = (γ(h_i))^{-2}

`'plain'`

  w_i = 1 for all i.

`'sqrt.nr'`

  w_i^2 equals the number of points n_i in bin i.

`'sd.inv'`

  1 / w_i equals the standard deviation of the variogram cloud within bin i.

`'internal'`

  Three subvariants are implemented:

  `'internal1'`

    w_i^2 = (N-i+1) n_i

  `'internal2'`

    w_i = N-i+1

  `'internal3'`

    w_i^2 = N-i+1

### Author(s)

Martin Schlather, schlather@math.uni-mannheim.de http://ms.math.uni-mannheim.de/de/publications/software

### See Also

`RFfit`, `RFfit-class`

### Examples

    RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
    ##                   RFoptions(seed=NA) to make them all random again
    ## see 'RFfit'

[Package RandomFields version 3.1.50 Index]