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\name{fitgauss}
\alias{fitgauss}
%\alias{AIC}
%\alias{AICc}
%\alias{logLik}
\title{Details on fitting Gaussian random fields, including Box-Cox transformation}
\description{
Here, some details of \command{\link{RFfit}} are given
concerning the fitting of models for Gaussian random fields.
\bold{ This documentation is far from being complete. }
}
% to do : merge with privat/rffitAdvanced.Rd
%\usage{}
%\arguments{}
%\value{}
\section{Maximum likelihood}{
The application of the usual maximum likelihood method and
reporting the result is the default.
}
%\section{Restricted maximum likelihood}{
% to do
%}
%\section{Composed likelihood}{
% to do
%}
\section{Least squares}{
The weighted least squares methods minimize
\deqn{
\sum_{i} w_i (\hat \gamma(h_i) - \gamma(h_i))^2
}
over all parametrized models of \eqn{\gamma}.
Here, \eqn{i} runs over all \eqn{N} bins of the binned variogram
\eqn{\hat \gamma}
and \eqn{h_i} is the centre of bin \eqn{i}.
The following variants of the least squares methods,
passed as \code{sub.methods} in \command{\link{RFfit}} are implemented:
\describe{
\item{\code{'self'}}{
\eqn{w_i = (\gamma(h_i))^{-2}}
}
\item{\code{'plain'}}{\eqn{w_i = 1} for all \eqn{i}.
}
\item{\code{'sqrt.nr'}}{\eqn{w_i^2} equals the number of points
\eqn{n_i} in bin \eqn{i}.
}
\item{\code{'sd.inv'}}{\eqn{1 / w_i} equals the standard deviation
of the variogram cloud within bin \eqn{i}.
}
\item{\code{'internal'}}{
Three subvariants are implemented:
\describe{
\item{\code{'internal1'}}{
\eqn{w_i^2 = (N-i+1) n_i }
}
\item{\code{'internal2'}}{
\eqn{w_i = N-i+1}
}
\item{\code{'internal3'}}{
\eqn{w_i^2 = N-i+1}
}
}
}
}
}
\seealso{
\code{\link{RFfit}}, \code{RFfit-class}.
}
\me
\keyword{spatial}
\keyword{optimize}
\examples{\dontshow{StartExample()}
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
## See 'RFfit'.
\dontshow{FinalizeExample()}}
|
