lmrob.lar: Least Absolute Residuals / L1 Regression

In robustbase: Basic Robust Statistics

Least Absolute Residuals / L1 Regression

Description

To compute least absolute residuals (LAR) or “L1” regression, lmrob.lar implements the routine L1 in Barrodale and Roberts (1974), which is based on the simplex method of linear programming. It is a copy of lmRob.lar (in early 2012) from the robust package.

Usage

lmrob.lar(x, y, control, ...)

Arguments

x	numeric matrix for the predictors.
y	numeric vector for the response.
control	list as returned by lmrob.control() .
...	(unused but needed when called as init(x,y,ctrl, mf) from lmrob())

Details

This method is used for computing the M-S estimate and typically not to be used on its own.

A description of the Fortran subroutines used can be found in Marazzi (1993). In the book, the main method is named RILARS.

Value

A list that includes the following components:

coef	The L1-estimate of the coefficient vector
scale	The residual scale estimate (mad)
resid	The residuals
iter	The number of iterations required by the simplex algorithm
status	Return status (0: optimal, but non unique solution, 1: optimal unique solution)
converged	Convergence status (always TRUE), needed for lmrob.fit.

Author(s)

Manuel Koller

References

Marazzi, A. (1993). Algorithms, routines, and S functions for robust statistics. Wadsworth & Brooks/Cole, Pacific Grove, CA.

See Also

rq from CRAN package quantreg.

Examples

data(stackloss)
X <- model.matrix(stack.loss ~ . , data = stackloss)
y <- stack.loss
(fm.L1 <- lmrob.lar(X, y))
with(fm.L1, stopifnot(converged
  , status == 1L
  , all.equal(scale, 1.5291576438)
  , sum(abs(residuals) < 1e-15) == 4 # p=4 exactly fitted obs.
))

robustbase documentation built on Sept. 27, 2024, 5:09 p.m.