# fitgauss: Details on fitting Gaussian random fields, including Box-Cox... In RandomFields: Simulation and Analysis of Random Fields

## 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 minimize

∑_{i} w_i (\hat γ(h_i) - γ(h_i))^2

over all parametrized 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

RFfit, RFfit-class.
 1 2 3 RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set ## RFoptions(seed=NA) to make them all random again ## See 'RFfit'.