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Quantile regression is a statistical technique intended to estimate,
and conduct inference about, conditional quantile functions.
Just as classical linear regression methods based on
minimizing sums of squared residuals enable one to estimate models for
conditional mean functions, quantile regression methods offer a mechanism
for estimating models for the conditional median function, and the full
range of other conditional quantile functions.
By supplementing the estimation of conditional mean functions with
techniques for estimating an entire family of conditional quantile
functions, quantile regression is capable of providing a more
complete statistical analysis of the stochastic relationships among
random variables.
Two elementary introductions to quantile regression:
Koenker, R. and K. Hallock, (2001)
Quantile Regression, Journal of Economic Perspectives, 15, 143-156.
Cade, B. and B. Noon, (2003)
A Gentle Introduction to Quantile Regression for Ecologists.
Frontiers in Ecology and the Environment, 1, 412-420.
A more extended treatment of the subject is now also available:
Koenker, R. (2005)
Quantile Regression, Econometric Society Monograph Series, Cambridge University Press.
Errata list.
Quantile regression software is now available in most modern statistical languages.
The recommended statistical language for quantile regression applications
is R. R is a open source
software project built on foundations of the S language of John Chambers.
Capabilities for quantile regression are provided by the
"quantreg" package. Once R is installed on a networked machine
packages can be easily installed using the command
install.packages("quantreg") in an R session.
The documention for the quantreg package for R is available in pdf format
from the CRAN website. A
vignette describing the functionality of the quantreg package is also available.
Some frequently asked questions about the quantreg package are answered in the
FAQ.
A basic version of the interior point (Frisch-Newton) algorithm for quantile regression
developed for the R quantreg package is also available for
matlab.
A C++ translation of the algorithm is also available from Ron Gallant's
libcpp library.
This algorithm is described in Koenker and Portnoy (Statistical Science, 1997).
Quantile regression is also available in the standard distributions of Stata,
Shazam, and a number of other statistical/econometric packages.
The Xplore
language includes quantile regression functions based on the
R code mentioned above.
SAS now also includes a quantreg procedure modeled closely on the R quantreg
package.
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