https://github.com/cran/quantreg
Revision 4cc4e6103f0362d98bad0a8826370ccbb5e9c7cf authored by Roger Koenker on 02 September 2012, 00:00:00 UTC, committed by Gabor Csardi on 02 September 2012, 00:00:00 UTC
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Tip revision: 4cc4e6103f0362d98bad0a8826370ccbb5e9c7cf authored by Roger Koenker on 02 September 2012, 00:00:00 UTC
version 4.85
version 4.85
Tip revision: 4cc4e61
rq.process.object.Rd
\name{rq.process.object}
\alias{rq.process.object}
\title{
Linear Quantile Regression Process Object
}
\description{
These are objects of class \code{rq.process.}
They represent the fit of a linear conditional quantile function model.
}
\section{Generation}{
This class of objects is returned from the \code{rq}
function
to represent a fitted linear quantile regression model.
}
\section{Methods}{
The \code{"rq.process"} class of objects has
methods for the following generic
functions:
\code{effects}, \code{formula}
, \code{labels}
, \code{model.frame}
, \code{model.matrix}
, \code{plot}
, \code{predict}
, \code{print}
, \code{print.summary}
, \code{summary}
}
\section{Structure}{
The following components must be included in a legitimate \code{rq.process}
object.
\describe{
\item{\code{sol}}{
The primal solution array. This is a (p+3) by J matrix whose
first row contains the 'breakpoints'
\eqn{tau_1, tau_2, \dots, tau_J},
of the quantile function, i.e. the values in [0,1] at which the
solution changes, row two contains the corresponding quantiles
evaluated at the mean design point, i.e. the inner product of
xbar and \eqn{b(tau_i)}, the third row contains the value of the objective
function evaluated at the corresponding \eqn{tau_j}, and the last p rows
of the matrix give \eqn{b(tau_i)}. The solution \eqn{b(tau_i)} prevails from
\eqn{tau_i} to \eqn{tau_i+1}. Portnoy (1991) shows that
\eqn{J=O_p(n \log n)}{J=O_p(n log n)}.
}
\item{\code{dsol}}{
The dual solution array. This is a
n by J matrix containing the dual solution corresponding to sol,
the ij-th entry is 1 if \eqn{y_i > x_i b(tau_j)}, is 0 if \eqn{y_i < x_i
b(tau_j)}, and is between 0 and 1 otherwise, i.e. if the
residual is zero. See Gutenbrunner and Jureckova(1991)
for a detailed discussion of the statistical
interpretation of dsol. The use of dsol in inference is described
in Gutenbrunner, Jureckova, Koenker, and Portnoy (1994).
}
}
}
\details{
These arrays are computed by parametric linear programming methods
using using the exterior point (simplex-type) methods of the
Koenker--d'Orey algorithm based on Barrodale and Roberts median
regression algorithm.
}
\references{
[1] Koenker, R. W. and Bassett, G. W. (1978). Regression quantiles,
\emph{Econometrica}, \bold{46}, 33--50.
[2] Koenker, R. W. and d'Orey (1987, 1994).
Computing Regression Quantiles.
\emph{Applied Statistics}, \bold{36}, 383--393, and \bold{43}, 410--414.
[3] Gutenbrunner, C. Jureckova, J. (1991).
Regression quantile and regression rank score process in the
linear model and derived statistics, \emph{Annals of Statistics},
\bold{20}, 305--330.
[4] Gutenbrunner, C., Jureckova, J., Koenker, R. and
Portnoy, S. (1994) Tests of linear hypotheses based on regression
rank scores. \emph{Journal of Nonparametric Statistics},
(2), 307--331.
[5] Portnoy, S. (1991). Asymptotic behavior of the number of regression
quantile breakpoints, \emph{SIAM Journal of Scientific
and Statistical Computing}, \bold{12}, 867--883.
}
\seealso{
\code{\link{rq}}.
}
\keyword{regression}
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