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\name{psi_func-class}
\docType{class}
\alias{psi_func-class}
\title{Class of "Psi Functions" for M-Estimation}
%% 'psi_func' cannot be used in title!
\description{
The class \code{"psi_func"} is used to store \eqn{\psi \ (psi)}{psi}
functions for M-estimation. In particular, an object of the class
contains \eqn{\rho(x) \ (\code{rho})}{rho(x)}, its derivative
\eqn{\psi(x) \ (psi)}{psi(x)}, the weight function \eqn{\psi(x)/x}, and
first derivative of \eqn{\psi}, \code{Dpsi = } \eqn{\psi'(x)}.
}
\section{Objects from the Class}{
Objects can be created by calls of the form \code{new("psi_func", ...)},
but preferably by \code{\link{psiFunc}(...)}.
}
\section{Slots}{
\describe{
\item{\code{rho}:}{the \eqn{\rho()}{rho()} function, an object of
class \code{"functionX"}. This is used to formulate the
objective function; \eqn{\rho()} can be regarded as generalized
negative log-likelihood.}
\item{\code{psi}:}{\eqn{\psi()}{psi()} is the derivative of \eqn{\rho},
\eqn{\psi(x) = \frac{d}{dx} \rho(x)}{psi(x) = d/dx rho(x)};
also of class \code{"functionX"}.}
\item{\code{wgt}:}{The weight function \eqn{\psi(x)/x},
of class \code{"functionX"}.}
\item{\code{Dpsi}:}{the derivative of \eqn{\psi},
\eqn{Dpsi(x) = psi'(x)}; of class \code{"functionX"}.}
\item{\code{Dwgt}:}{the derivative of the weight function,
of class \code{"functionX"}, is generated automatically if
\code{\link{psiFunc}} constructor is used.}
\item{\code{tDefs}:}{\emph{named} numeric vector of \bold{t}uning
parameter \bold{Def}ault values.}
%%% FIXME : Replace these by *methods*
\item{\code{Erho}:}{A function of class \code{"functionXal"} for
computing \eqn{E[\rho(X)]} when \eqn{X} is standard normal
\eqn{\mathcal{N}(0,1)}{N(0,1)}.}
\item{\code{Epsi2}:}{A function of class \code{"functionXal"} for
computing \eqn{E[\psi^2(X)]} when \eqn{X} is standard normal.}
\item{\code{EDpsi}:}{A function of class \code{"functionXal"} for
computing \eqn{E[\psi'(X)]} when \eqn{X} is standard normal.}
\item{\code{name}:}{Name of \eqn{\psi}{psi}-function used for printing.}
\item{\code{xtras}:}{Potentially further information.}
}
}
\section{Methods}{
Currently, only \code{\link{chgDefaults}()}, \code{\link[=plot-methods]{plot}()}
and \code{show()}.
}
\author{Martin Maechler}
\seealso{
\code{\link{psiFunc}}.
}
\examples{
str(huberPsi, give.attr = FALSE)
plot(hampelPsi)# calling the plot method (nicely showing "all" !)
}
\keyword{classes}
\keyword{robust}
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