# rq.fit.fnb

0th

Percentile

##### 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.

Keywords
regression
##### Usage
rq.fit.fnb(x, y, tau=0.5, rhs = (1-tau)*apply(x,2,sum), beta=0.99995, eps=1e-06)
##### Arguments
x

The design matrix

y

The response vector

tau

The quantile of interest, must lie in (0,1)

rhs

The right hand size of the dual equality constraint, modify at your own risk.

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.

##### Details

The details of the 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 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. This function replaces an earlier one rq.fit.fn, which required the initial dual values to be feasible. This 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.

##### Value

returns an object of class "rq", which can be passed to summary.rq to obtain standard errors, etc.

##### References

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