\name{boot.crq}
\alias{boot.crq}
\title{ Bootstrapping Censored Quantile Regression}
\description{
Functions used to estimated standard errors, confidence
intervals and tests of hypotheses for censored quantile regression models
using the Portnoy and Peng-Huang methods.  }
\usage{
boot.crq(x, y, c, taus, method, ctype = "right", R = 100, mboot, bmethod = "Bose", ...)
}
\arguments{
  \item{x}{ The regression design matrix}
  \item{y}{ The regression response vector}
  \item{c}{ The censoring indicator}
  \item{taus}{ The quantiles of interest}
  \item{method}{ The fitting method: either "P" for Portnoy or "PH" for Peng and Huang.}
  \item{ctype}{ Either "right" or "left"}
  \item{R}{ The number of bootstrap replications}
  \item{bmethod}{ The method to be employed.  There are (as yet) two
	options:  method = "xy-pair" uses the xy-pair method, that is
	the usual multinomial resampling of xy-pairs, while  method
	= "Bose" uses the Bose and Chatterjee (2003) weighted resampling
	method with exponential weights. This is now the default.}
  \item{mboot}{ optional argument for the bootstrap method "xy-pair" that
	permits subsampling (m out of n) bootstrap.  Obviously mboot
	should be substantially larger than the column dimension of x,
	and should be less than the sample size.}
  \item{...}{ Optional further arguments to control bootstrapping}
}
\details{
There are several refinements that are still unimplemented.  Percentile
methods should be incorporated, and extensions of the methods to be used 
in anova.rq should be made.  Note that bootstrapping for the Powell 
method "FP" is done via \code{\link{boot.rq}}.
}
\value{
  A matrix of dimension R by p is returned with the R resampled
  estimates of the vector of quantile regression parameters. When
  mofn < n for the "xy" method this matrix has been deflated by
  the fact sqrt(m/n)
}
\references{ 
 Bose, A. and S. Chatterjee, (2003) Generalized bootstrap for estimators
        of minimizers of convex functions, \emph{J. Stat. Planning and Inf}, 117,
        225-239.

}

\author{ Roger Koenker }
\seealso{  \code{\link{summary.crq}}}
\keyword{ regression}