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\name{lmrob.fit}
\alias{lmrob.fit}
\alias{lmrob.fit.MM}
\title{ MM-type estimator for regression }
\description{
Compute MM-type estimators of regression: An S-estimator is
used as starting value, and an M-estimator with fixed scale and
redescending psi-function is used from there. Optionally a D-step
(Design Adaptive Scale estimate) as well as a second M-step is
calculated.
}
\usage{
lmrob.fit(x, y, control, init = NULL, mf = NULL, bare.only = FALSE)
}
\arguments{
\item{x}{design matrix (\eqn{n \times p}{n x p}) typically including a
column of \code{1}s for the intercept.}
\item{y}{numeric response vector (of length \eqn{n}).}
\item{control}{a list of control parameters as returned
by \code{\link{lmrob.control}}, used for both the initial S-estimate
and the subsequent M- and D-estimates.}
\item{init}{optional \code{\link{list}} of initial estimates. See
\emph{Details}.}
\item{mf}{defunct.}
\item{bare.only}{logical indicating if the result should be
\code{\link{return}()}ed after the bare computation steps are done.
Useful, e.g., when you only need the \code{coefficients}.}
}
\details{This function is the basic fitting function for MM-type estimation,
called by \code{\link{lmrob}} and typically not to be used on its own.
If given, \code{init} must be a list of initial estimates containing
at least the initial coefficients and scale as \code{coefficients} and
\code{scale}. Otherwise it calls \code{\link{lmrob.S}(..)} and uses it
as initial estimator.
}
\value{
A list with components (some missing in case \code{bare.only} is true)
\item{fitted.values}{\eqn{X \beta}{X beta}, i.e., \code{X \%*\% coefficients}.}
\item{residuals}{the raw residuals, \code{y - fitted.values}}
\item{rweights}{robustness weights derived from the final M-estimator
residuals (even when not converged).}
\item{rank}{}
\item{degree.freedom}{\code{n - rank}}% more!
\item{coefficients}{estimated regression coefficient vector}
\item{scale}{the robustly estimated error standard deviation}% = final.MM$scale,
\item{cov}{variance-covariance matrix of \code{coefficients}, if the
RWLS iterations have converged (and \code{control$cov} is not \code{"none"}).}
\item{control}{}% = control,
\item{iter}{}% = final.MM$iter, <<<<<< also 'init.S' !
\item{converged}{logical indicating if the RWLS iterations have converged.}
\item{init.S}{the whole initial S-estimator result, including its own
\code{converged} flag, see \code{\link{lmrob.S}} (only for MM-estimates).}
\item{init}{A similar list that contains the results of intermediate
estimates (not for MM-estimates).}
}
\author{ Matias Salibian-Barrera, Martin Maechler and Manuel Koller}
\seealso{
\code{\link{lmrob}},
\code{\link{lmrob..M..fit}},
\code{\link{lmrob..D..fit}},
\code{\link{lmrob.S}}
}
\keyword{robust}
\keyword{regression}
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