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\name{nlrob-algorithms}
\alias{nlrob.algorithms}
\alias{nlrob.MM}
\alias{nlrob.tau}
\alias{nlrob.CM}
\alias{nlrob.mtl}
\title{MM-, Tau-, CM-, and MTL- Estimators for Nonlinear Robust Regression}
\description{
\describe{
\item{"MM":}{Compute an MM-estimator for nonlinear robust (constrained)
regression.}
\item{"tau":}{Compute a Tau-estimator for nonlinear robust (constrained)
regression.}
\item{"CM":}{Compute a \dQuote{Constrained M} (=: CM) estimator for
nonlinear robust (constrained) regression.}
\item{"MTL":}{Compute a \dQuote{Maximum Trimmed Likelihood} (=: MTL)
estimator for nonlinear robust (constrained) regression.}
}
}
\usage{
## You can *not* call the nlrob(*, method = <M>) like this ==> see help(nlrob)
## ------- ===== ------------------------------------------
nlrob.MM(formula, data, lower, upper,
tol = 1e-06,
psi = c("bisquare", "lqq", "optimal", "hampel"),
init = c("S", "lts"),
ctrl = nlrob.control("MM", psi = psi, init = init, fnscale = NULL,
tuning.chi.scale = .psi.conv.cc(psi, .Mchi.tuning.defaults[[psi]]),
tuning.psi.M = .psi.conv.cc(psi, .Mpsi.tuning.defaults[[psi]]),
optim.control = list(), optArgs = list(...)),
...)
nlrob.tau(formula, data, lower, upper,
tol = 1e-06, psi = c("bisquare", "optimal"),
ctrl = nlrob.control("tau", psi = psi, fnscale = NULL,
tuning.chi.scale = NULL, tuning.chi.tau = NULL,
optArgs = list(...)),
...)
nlrob.CM(formula, data, lower, upper,
tol = 1e-06,
psi = c("bisquare", "lqq", "welsh", "optimal", "hampel", "ggw"),
ctrl = nlrob.control("CM", psi = psi, fnscale = NULL,
tuning.chi = NULL, optArgs = list(...)),
...)
nlrob.mtl(formula, data, lower, upper,
tol = 1e-06,
ctrl = nlrob.control("mtl", cutoff = 2.5, optArgs = list(...)),
...)
}
\arguments{
\item{formula}{nonlinear regression \code{\link{formula}}, using both
variable names from \code{data} and parameter names from either
\code{lower} or \code{upper}.}
\item{data}{data to be used, a \code{\link{data.frame}}}
\item{lower, upper}{bounds aka \dQuote{box constraints} for all the
parameters, in the case "CM" and "mtl" these must include the error
standard deviation as \code{"sigma"}, see \code{\link{nlrob}()}
about its \code{\link{names}}, etc.
Note that one of these two must be a properly \dQuote{named}, e.g.,
\code{names(lower)} being a \code{\link{character}} vector of parameter names
(used in \code{formula} above).
}
\item{tol}{numerical convergence tolerance.}
\item{psi, init}{see \code{\link{nlrob.control}}.}
\item{ctrl}{a \code{\link{list}}, typically the result of a call to
\code{\link{nlrob.control}}.}
\item{tuning.psi.M}{..}% FIXME
\item{optim.control}{..}% FIXME
\item{optArgs}{a \code{\link{list}} of optional arguments for
optimization, e.g., \code{trace = TRUE}, passed to to the optimizer,
which currently must be \code{\link[DEoptimR]{JDEoptim}(.)}.}
\item{...}{alternative way to pass the \code{optArgs} above.}
}
\value{
an \R object of \code{\link{class}} \code{"nlrob.<meth>"}, basically a
list with components
%% FIXME
}
\details{
Copyright 2013, Eduardo L. T. Conceicao. Available under
the GPL (>= 2)
Currently, all four methods use \code{\link[DEoptimR]{JDEoptim}()}
from \CRANpkg{DEoptimR}, which subsamples using \code{\link{sample}()}.
From \R version 3.6.0, \code{\link{sample}} depends on
\code{\link{RNGkind}(*, sample.kind)}, such that exact reproducibility of
results from \R versions 3.5.3 and earlier requires setting
\code{\link{RNGversion}("3.5.0")}.
In any case, do use \code{\link{set.seed}()} additionally for reproducibility!
}
\author{
Eduardo L. T. Conceicao; compatibility (to \code{\link{nlrob}})
tweaks and generalizations, inference, by Martin Maechler.
}
\source{
For \code{"MTL"}:
Maronna, Ricardo A., Martin, R. Douglas, and Yohai, Victor J. (2006).
\emph{Robust Statistics: Theory and Methods} Wiley, Chichester, p. 133.
}
\references{
\describe{
\item{"MM":}{
Yohai, V.J. (1987)
High breakdown-point and high efficiency robust estimates for
regression.
\emph{The Annals of Statistics} \bold{15}, 642--656.
}
\item{"tau":}{
Yohai, V.J., and Zamar, R.H. (1988).
High breakdown-point estimates of regression by means of the
minimization of an efficient scale.
\emph{Journal of the American Statistical Association} \bold{83},
406--413.
}
\item{"CM":}{
Mendes, B.V.M., and Tyler, D.E. (1996)
Constrained M-estimation for regression.
In: \emph{Robust Statistics, Data Analysis and Computer Intensive
Methods}, Lecture Notes in Statistics 109, Springer, New York, 299--320.
%% not yet -- e.g. tuning constants for Welsh:
%% Edlund, O. and Ekblom, H. (2005)
%% Computing the constrained M-estimates for regression.
%% Computational Statistics Data Analysis \bold{49}(1): 19--32.
}
\item{"MTL":}{
Hadi, Ali S., and Luceno, Alberto (1997).
Maximum trimmed likelihood estimators: a unified approach,
examples, and algorithms.
Computational Statistics & Data Analysis \bold{25}, 251--272.
Gervini, Daniel, and Yohai, Victor J. (2002).
A class of robust and fully efficient regression estimators.
The Annals of Statistics \bold{30}, 583--616.
}
}%describe
}
\examples{%% for more, --> ../tests/nlregrob-tst.R
DNase1 <- DNase[DNase$Run == 1,]
form <- density ~ Asym/(1 + exp(( xmid -log(conc) )/scal ))
pnms <- c("Asym", "xmid", "scal")
set.seed(47) # as these by default use randomized optimization:
fMM <- robustbase:::nlrob.MM(form, data = DNase1,
lower = setNames(c(0,0,0), pnms), upper = 3,
## call to nlrob.control to pass 'optim.control':
ctrl = nlrob.control("MM", optim.control = list(trace = 1),
optArgs = list(trace = TRUE)))
## The same via nlrob() {recommended; same random seed to necessarily give the same}:
set.seed(47)
gMM <- nlrob(form, data = DNase1, method = "MM",
lower = setNames(c(0,0,0), pnms), upper = 3, trace = TRUE)
gMM
summary(gMM)
## and they are the same {apart from 'call' and 'ctrl' and new stuff in gMM}:
ni <- names(fMM); ni <- ni[is.na(match(ni, c("call","ctrl")))]
stopifnot(all.equal(fMM[ni], gMM[ni]))
\dontshow{
if(doExtras <- robustbase:::doExtras()) {
gtau <- nlrob(form, data = DNase1, method = "tau",
lower = setNames(c(0,0,0), pnms), upper = 3, trace = TRUE)
## these two have "sigma" also as parameter :
psNms <- c(pnms, "sigma")
gCM <- nlrob(form, data = DNase1, method = "CM",
lower = setNames(c(0,0,0,0), psNms), upper = 3, trace = TRUE)
gmtl <- nlrob(form, data = DNase1, method = "mtl",
lower = setNames(c(0,0,0,0), psNms), upper = 3, trace = TRUE)
stopifnot(identical(sapply(list(gMM, gCM, gmtl), estimethod),
c("MM", "CM", "mtl")))
}% doExtras
}% dontshow
}
\keyword{robust}
\keyword{regression}
\keyword{nonlinear}
|
