swh:1:snp:16c54c84bc54885e783d4424d714e5cc82f479a1
Tip revision: 6d5057a2e46105744eb4d62fcdc6610efeedb017 authored by Roger Koenker on 01 December 2011, 00:00:00 UTC
version 4.76
version 4.76
Tip revision: 6d5057a
summary.rq.Rd
\name{summary.rq}
\alias{summary.rq}
\alias{summary.rqs}
\alias{summary.rcrqs}
\title{
Summary methods for Quantile Regression
}
\description{
Returns a summary list for a quantile regression fit. A null value
will be returned if printing is invoked.
}
\usage{
\method{summary}{rq}(object, se = NULL, covariance=FALSE, hs = TRUE, ...)
\method{summary}{rqs}(object, ...)
}
\arguments{
\item{object}{
This is an object of class \code{"rq"} or \code{"rqs"} produced by
a call to \code{rq()}, depending on whether one or more taus are
specified.
}
\item{se}{
specifies the method used to compute standard standard errors. There
are currently five available methods:
\enumerate{
\item \code{"rank"} which produces confidence intervals for the
estimated parameters by inverting a rank test as described in
Koenker (1994). The default option assumes that the errors are
iid, while the option iid = FALSE implements the proposal of Koenker
Machado (1999).
See the documentation for \code{rq.fit.br} for additional arguments.
\item \code{"iid"} which presumes that the errors are iid and computes
an estimate of the asymptotic covariance matrix as in KB(1978).
\item \code{"nid"} which presumes local (in \code{tau})
linearity (in \code{x}) of the
the conditional quantile functions and computes a Huber
sandwich estimate using a local estimate of the sparsity.
\item \code{"ker"} which uses a kernel estimate of the sandwich
as proposed by Powell(1990).
\item \code{"boot"} which implements one of several possible bootstrapping
alternatives for estimating standard errors.
}
If \code{se = NULL} (the default) and \code{covariance = FALSE}
then the "rank" method is used, otherwise the "nid" method is used.
}
\item{covariance}{
logical flag to indicate whether the full covariance matrix of the
estimated parameters should be returned.
}
\item{hs}{
Use Hall Sheather bandwidth for sparsity estimation
If false revert to Bofinger bandwidth.
}
\item{...}{
Optional arguments to summary, e.g. bsmethod to use bootstrapping.
see \code{\link{boot.rq}}
}
}
\value{
a list is returned with the following components, when \code{object}
is of class \code{"rqs"} then there is a list of such lists.
\item{coefficients}{
a p by 4 matrix consisting of the coefficients, their estimated standard
errors, their t-statistics, and their associated p-values.
}
\item{cov}{
the estimated covariance matrix for the coefficients in the model,
provided that \code{cov=TRUE} in the called sequence.
}
\item{Hinv}{
inverse of the estimated Hessian matrix returned if \code{cov=TRUE} and
\code{se \%in\% c("nid","ker") }, note that for \code{se = "boot"} there
is no way to split the estimated covariance matrix into its sandwich
constituent parts.
}
\item{J}{
Unscaled Outer product of gradient matrix returned if \code{cov=TRUE} and \code{se
!= "iid"}. The Huber sandwich is \code{cov = tau (1-tau) Hinv \%*\% J \%*\% Hinv}.
as for the \code{Hinv} component, there is no \code{J} component when
\code{se == "boot"}. (Note that to make the Huber sandwich you need to add the
tau (1-tau) mayonnaise yourself.)
}
}
\details{
When the default summary method is used, it tries to estimate a sandwich
form of the asymptotic covariance matrix and this involves estimating
the conditional density at each of the sample observations, negative
estimates can occur if there is crossing of the neighboring quantile
surfaces used to compute the difference quotient estimate.
A warning message is issued when such negative estimates exist indicating
the number of occurrences -- if this number constitutes a large proportion
of the sample size, then it would be prudent to consider an alternative
inference method like the bootstrap.
If the number of these is large relative to the sample size it is sometimes
an indication that some additional nonlinearity in the covariates
would be helpful, for instance quadratic effects.
Note that the default \code{se} method is rank, unless the sample size exceeds
1001, in which case the \code{rank} method is used.
}
\references{
Koenker, R. (2004) \emph{Quantile Regression}.
Bilias, Y. Chen, S. and Z. Ying, Simple resampling methods for censored
quantile regression, \emph{J. of Econometrics}, 99, 373-386.
}
\seealso{
\code{\link{rq}}
\code{\link{bandwidth.rq}}
}
\examples{
data(stackloss)
y <- stack.loss
x <- stack.x
summary(rq(y ~ x, method="fn")) # Compute se's for fit using "nid" method.
summary(rq(y ~ x, ci=FALSE),se="ker")
# default "br" alg, and compute kernel method se's
}
\keyword{regression}