rq.fit.fnc {quantreg}  R Documentation 
This is a lower level routine called by rq()
to compute quantile
regression methods using the FrischNewton algorithm. It allows the
call to specify linear inequality constraints to which the fitted
coefficients will be subjected.
rq.fit.fnc(x, y, R, r, tau=0.5, beta=0.9995, eps=1e06)
x 
The design matrix 
y 
The response vector 
R 
The matrix describing the inequality constraints 
r 
The right hand side vector of inequality constraints 
tau 
The quantile of interest, must lie in (0,1) 
beta 
technical step length parameter – alter at your own risk! 
eps 
tolerance parameter for convergence. In cases of multiple optimal solutions
there may be some discrepancy between solutions produced by method
"fn" and method "br" . This is due to the fact that
"fn" tends to converge to a point near the centroid of the
solution set, while "br" stops at a vertex of the set.

The details of the algorithm are explained in Koenker and Ng (2002).
The basic idea can be traced back to the logbarrier methods proposed by
Frisch in the 1950's for constrained optimization. But the current
implementation is based on proposals by Mehrotra and others in the
recent (explosive) literature on interior point methods for solving linear
programming problems. See "rq"
helpfile for an example.
returns an object of class "rq"
, which can be passed to
summary.rq
to obtain standard errors, etc. It is
an open research problem to provide an inference apparatus for
inequality constrained quantile regression.
Koenker, R. and S. Portnoy (1997). The Gaussian Hare and the Laplacian Tortoise: Computability of squarederror vs. absoluteerror estimators, with discussion, Statistical Science, 12, 279300.
Koenker, R. and P. Ng(2002). Inequality Constrained Quantile Regression, in process