\name{summary.rq}
\alias{summary.rq}
\title{
Summary method for Quantile Regression
}
\description{
Returns a summary list for a quantile regression fit.  A null value
will be returned if printing is invoked.
}
\usage{
summary.rq(object, se="nid", covariance=T, hs = T, ...)
}
\arguments{
  \item{object}{
    This is an object of class \code{"rq"} produced by a call to \code{rq()}.
  }
  \item{se}{
    specifies the method used to compute standard standard errors.  There
    are currently three available methods:  
    \enumerate{
      \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{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
   }
}
\value{
  a list is returned with the following components

\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=T} in the called sequence.
}
\item{Hinv}{
  inverse of the estimated Hessian matrix returned if \code{cov=T} and
  \code{se != "iid"}.
}
\item{J}{
  Outer product of gradient matrix returned if \code{cov=T} and \code{se
    != "iid"}. The Huber sandwich is \code{cov = Hinv \%*\% J \%*\% Hinv}.
}}
\references{
  Koenker, R. (2000) \emph{Quantile Regression}.
}
\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=F),se="ker")
# default "br" alg, and compute kernel method se's
}
\keyword{regression}
% Converted by Sd2Rd version 0.3-3.