This is a lower level routine called by rq() to compute quantile
regression parameters using the Frisch-Newton algorithm. In contrast to
method "fn" it computes solutions for all the specified taus inside a
fortran loop. See rq.fit.pfnb for further details on a more
efficient preprocessing method.
rq.fit.qfnb(x, y, tau)returns a list with elements consisting of
a matrix of dimension ncol(x) by length(taus)
a 3-vector of iteration counts
a convergence flag
The design matrix
The response vector
The quantiles of interest, must lie in (0,1), be sorted and preferably equally spaced.
The details of the Frisch-Newton algorithm are explained in Koenker and Portnoy (1997).
The basic idea can be traced back to the log-barrier methods proposed by
Frisch in the 1950's for linear programming. 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. This function replaces an earlier one rq.fit.fn,
which required the initial dual values to be feasible. The current version allows the
user to specify an infeasible starting point for the dual problem, that
is one that may not satisfy the dual equality constraints. It still
assumes that the starting value satisfies the upper and lower bounds.
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.
rq, rq.fit.br,
rq.fit.pfn