swh:1:snp:16c54c84bc54885e783d4424d714e5cc82f479a1
Tip revision: db8668b63745f624236e566437c198010990b082 authored by Roger Koenker on 02 May 2022, 16:42:02 UTC
version 5.93
version 5.93
Tip revision: db8668b
rqss.object.Rd
\name{rqss.object}
\alias{rqss.object}
\alias{logLik.rqss}
\alias{AIC.rqss}
\alias{fitted.rqss}
\alias{resid.rqss}
\alias{print.rqss}
\title{RQSS Objects and Summarization Thereof}
\description{
Functions to reveal the inner meaning of objects created by \code{rqss} fitting.
}
\usage{
\method{logLik}{rqss}(object, ...)
\method{AIC}{rqss}(object, ..., k=2)
\method{print}{rqss}(x, ...)
\method{resid}{rqss}(object, ...)
\method{fitted}{rqss}(object, ...)
}
\arguments{
\item{object}{an object returned from \code{rqss} fitting, describing
an additive model estimating a conditional quantile function.
See \code{\link{qss}} for details on how to specify these terms.}
\item{x}{an rqss object, as above.}
\item{k}{a constant factor governing the weight attached to the penalty
term on effective degrees of freedom of the fit. By default
k =2 corresponding to the Akaike version of the penalty, negative
values indicate that the k should be set to log(n) as proposed
by Schwarz (1978).}
\item{...}{additional arguments}
}
\details{ Total variation regularization for univariate and
bivariate nonparametric quantile smoothing is described
in Koenker, Ng and Portnoy (1994) and Koenker and Mizera(2003)
respectively. The additive model extension of this approach
depends crucially on the sparse linear algebra implementation
for R described in Koenker and Ng (2003). Eventually, these
functions should be expanded to provide an automated lambda
selection procedure.}
\value{
The function \code{summary.rqss} returns a list consisting of
the following components:
\item{fidelity}{Value of the quantile regression objective function.}
\item{penalty}{A list consisting of the values of the total variation
smoothing penalty for each of additive components.}
\item{edf}{Effective degrees of freedom of the fitted model, defined
as the number of zero residuals of the fitted model, Koenker
Mizera (2003) for details.}
\item{qssedfs}{A list of effective degrees of freedom for each of
the additive components of the fitted model, defined as the
number of non-zero elements of each penalty component of the
residual vector.}
\item{lamdas}{A list of the lambdas specified for each of the additive
components of the model.}
}
\references{
[1] Koenker, R. and S. Portnoy (1997)
The Gaussian Hare and the Laplacean
Tortoise: Computability of Squared-error vs Absolute Error Estimators,
(with discussion).
\emph{Statistical Science} \bold{12}, 279--300.
[2] Koenker, R., P. Ng and S. Portnoy, (1994)
Quantile Smoothing Splines;
\emph{Biometrika} \bold{81}, 673--680.
[3] Koenker, R. and I. Mizera, (2003)
Penalized Triograms: Total Variation Regularization for Bivariate Smoothing;
\emph{JRSS(B)} \bold{66}, 145--163.
[4] Koenker, R. and P. Ng (2003)
SparseM: A Sparse Linear Algebra Package for R,
\emph{J. Stat. Software}.
}
\author{ Roger Koenker }
\seealso{ \code{\link{plot.rqss}}
}
\examples{
require(MatrixModels)
n <- 200
x <- sort(rchisq(n,4))
z <- x + rnorm(n)
y <- log(x)+ .1*(log(x))^2 + log(x)*rnorm(n)/4 + z
plot(x, y-z)
f.N <- rqss(y ~ qss(x, constraint= "N") + z)
f.I <- rqss(y ~ qss(x, constraint= "I") + z)
f.CI <- rqss(y ~ qss(x, constraint= "CI") + z)
lines(x[-1], f.N $coef[1] + f.N $coef[-(1:2)])
lines(x[-1], f.I $coef[1] + f.I $coef[-(1:2)], col="blue")
lines(x[-1], f.CI$coef[1] + f.CI$coef[-(1:2)], col="red")
## A bivariate example
if(requireNamespace("tripack")){
if(requireNamespace("akima")){
data(CobarOre)
fCO <- rqss(z ~ qss(cbind(x,y), lambda= .08), data=CobarOre)
plot(fCO)
}}}
\keyword{regression}
\keyword{smooth}
\keyword{robust}