rq.fit.qfnb: Quantile Regression Fitting via Interior Point Methods

In quantreg: Quantile Regression

Quantile Regression Fitting via Interior Point Methods

Description

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.

Usage

rq.fit.qfnb(x, y, tau)

Arguments

x	The design matrix
y	The response vector
tau	The quantiles of interest, must lie in (0,1), be sorted and preferably equally spaced.

Details

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.

Value

returns a list with elements consisting of

1. coefficientsa matrix of dimension ncol(x) by length(taus)

2. nit a 3-vector of iteration counts

3. info a convergence flag

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.

See Also

rq, rq.fit.br, rq.fit.pfn

quantreg documentation built on Aug. 19, 2023, 5:09 p.m.