Revision 6599e015b196d3220041ffaf64414375c87d5be5 authored by Roger Koenker on 14 May 2016, 00:47:02 UTC, committed by cran-robot on 14 May 2016, 00:47:02 UTC
1 parent cba29df
boot.rq.Rd
\name{boot.rq}
\alias{boot.rq}
\alias{boot.rq.xy}
\alias{boot.rq.wxy}
\alias{boot.rq.pwy}
\alias{boot.rq.mcmb}
\title{ Bootstrapping Quantile Regression}
\description{
These functions can be used to construct standard errors, confidence
intervals and tests of hypotheses regarding quantile regression models.
}
\usage{
boot.rq(x, y, tau = 0.5, R = 200, bsmethod = "xy", mofn = length(y),
cluster = NULL, U = NULL, ...)
}
\arguments{
\item{x}{ The regression design matrix}
\item{y}{ The regression response vector}
\item{tau}{ The quantile of interest}
\item{R}{ The number of bootstrap replications}
\item{bsmethod}{ The method to be employed. There are (as yet) five
options: method = "xy" uses the xy-pair method, and
method = "pwy" uses the method of Parzen, Wei and Ying (1994)
method = "mcmb" uses the Markov chain marginal bootstrap
of He and Hu (2002) and Kocherginsky, He and Mu (2003).
The fourth method = "wxy" uses the generalized bootstrap
of Bose and Chatterjee (2003) with unit exponential weights,
see also Chamberlain and Imbens (2003). The fifth method
"wild" uses the wild bootstrap method proposed by Feng, He and Hu (2011). }
\item{mofn}{ optional argument for the bootstrap method "xy" that
permits subsampling (m out of n) bootstrap. Obviously mofn
should be substantially larger than the column dimension of x,
and should be less than the sample size.}
\item{cluster}{If non-NULL this argument should specify cluster id
numbers for each observation, in which case the clustered version of
the bootstrap based on the proposal of Hagemann (2016). If present
\code{bsmethod} is set to set to "cluster"}
\item{U}{If non-NULL this argument should specify an array of indices
or gradient evaluations to be used by the corresponding bootstrap
method as specified by \code{bsmethod}. This is NOT intended as
a user specified input, instead it is specified in \code{summary.rqs}
to ensure that bootstrap samples for multiple taus use the same
realizations of the random sampling.}
\item{...}{ Optional arguments to control bootstrapping}
}
\details{
Their 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.
}
\value{
A list consisting of two elements:
A matrix \code{B} 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 factor sqrt(m/n).
A matrix \code{U} of sampled indices (for \code{bsmethod in c("xy", "wxy")})
or gradient evaluations (for \code{bsmethod in c("pwy", "cluster")})
used to generate the bootstrapped realization, and potentially reused
for other \code{taus} when invoked from \code{summary.rqs}.
}
\references{
[1] Koenker, R. W. (1994). Confidence Intervals for regression quantiles, in
P. Mandl and M. Huskova (eds.), \emph{Asymptotic Statistics}, 349--359,
Springer-Verlag, New York.
[2] Kocherginsky, M., He, X. and Mu, Y. (2005).
Practical Confidence Intervals for Regression Quantiles,
Journal of Computational and Graphical Statistics, 14, 41-55.
[3] Hagemann, A. (2016) Cluster Robust Bootstrap inference in
quantile regression models, Journal of the American Statistical Association ,
forthcoming.
[4] He, X. and Hu, F. (2002). Markov Chain Marginal Bootstrap.
Journal of the American Statistical Association , Vol. 97, no. 459,
783-795.
[5] Parzen, M. I., L. Wei, and Z. Ying (1994): A resampling
method based on pivotal estimating functions,'' Biometrika, 81, 341--350.
[6] Bose, A. and S. Chatterjee, (2003) Generalized bootstrap for estimators
of minimizers of convex functions, \emph{J. Stat. Planning and Inf}, 117, 225-239.
[7] Chamberlain G. and Imbens G.W. (2003) Nonparametric Applications of
Bayesian Inference, Journal of Business & Economic Statistics, 21, pp. 12-18.
[8] Feng, Xingdong, Xuming He, and Jianhua Hu (2011) Wild Bootstrap for
Quantile Regression, Biometrika, to appear.
}
\author{ Roger Koenker (and Xuming He and M. Kocherginsky for the mcmb code)}
\seealso{ \code{\link{summary.rq}}}
\examples{
y <- rnorm(50)
x <- matrix(rnorm(100),50)
fit <- rq(y~x,tau = .4)
summary(fit,se = "boot", bsmethod= "xy")
summary(fit,se = "boot", bsmethod= "pwy")
#summary(fit,se = "boot", bsmethod= "mcmb")
}
\keyword{ regression}
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