Quantile Regression Fitting via Interior Point Methods
This is a lower level routine called by
rq() to compute quantile
regression methods using the Frisch-Newton algorithm. It allows the
call to specify linear inequality constraints to which the fitted
coefficients will be subjected. The constraints are assumed to be
formulated as Rb >= r.
rq.fit.fnc(x, y, R, r, tau=0.5, beta=0.9995, eps=1e-06)
The design matrix
The response vector
The matrix describing the inequality constraints
The right hand side vector of inequality constraints
The quantile of interest, must lie in (0,1)
technical step length parameter -- alter at your own risk!
tolerance parameter for convergence. In cases of multiple optimal solutions there may be some discrepancy between solutions produced by 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 log-barrier 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.
It is an open research problem to provide an inference apparatus for
inequality constrained quantile regression.
returns an object of class
"rq", which can be passed to
summary.rq to obtain standard errors, etc.
Koenker, R. and S. Portnoy (1997). The Gaussian Hare and the Laplacian Tortoise: Computability of squared-error vs. absolute-error estimators, with discussion, Statistical Science, 12, 279-300.
Koenker, R. and P. Ng(2005). Inequality Constrained Quantile Regression, Sankya, 418-440.