I'd like to mention that there is a new quantile regression package
"nprq" on CRAN for additive nonparametric quantile regression
estimation.
Models are structured similarly to the gss package of Gu and the mgcv
package of Wood. Formulae like
y ~ qss(z1) + qss(z2) + X
are interpreted as a partially linear model in the covariates of X,
with nonparametric components defined as functions of z1 and z2.
Rather than estimating conditional mean functions, conditional
quantile functions are estimated using penalty methods.
When z1 is univariate fitting is based on the total variation
penalty methods described in Koenker, Ng and Portnoy (Biometrika, 1994).
When z2 is bivariate fitting is based on the total variation penalty
(triogram) methods described in Koenker and Mizera (2003), available at
http://www.econ.uiuc.edu/~roger/research/goniolatry/gon.html and
forthcoming in JRSS(B).
There are options to constrain the qss components to be monotone and/or
convex/concave for univariate components, and to be convex/concave
for bivariate components. Fitting is done by new sparse implementations
of the dense interior point (Frisch-Newton) algorithms already available
in the package quantreg.
The new package "nprq" thus supplements the existing packages
"quantreg" and "nlrq" that can be used for linear and
nonlinear
parametric quantile regression fitting respectively. In particular,
"nprq" provides general fitting functions for quantile regression
problems with sparse design matrices paralleling the functionality of
least squares function slm() in the SparseM package.
There has also been some recent updating of the quantreg package, which
now includes some functionality for resampling based inference methods.
The package "nprq" is joint work with Pin Ng of Northern Arizona
University.
Comments and suggestions, as always, would be most welcome.
url: www.econ.uiuc.edu/~roger/my.html Roger Koenker
email rkoenker at uiuc.edu Department of Economics
vox: 217-333-4558 University of Illinois
fax: 217-244-6678 Champaign, IL 61820
