lmrob.S: S-regression estimators

In robustbase: Basic Robust Statistics

S-regression estimators

Description

Computes an S-estimator for linear regression, using the “fast S” algorithm.

Usage

lmrob.S(x, y, control,
        trace.lev = control$trace.lev,
        only.scale = FALSE, mf)

Arguments

x	design matrix (n \times p)
y	numeric vector of responses (or residuals for only.scale=TRUE).
control	list as returned by lmrob.control; the following components are used for lmrob.S(): "trace.lev", "nResample", "groups", "n.group", "fast.s.large.n", "seed", "bb", "psi", "tuning.chi", "best.r.s", "k.fast.s", "k.max", "maxit.scale", "refine.tol", "solve.tol", "scale.tol", "mts", "subsampling".
trace.lev	integer indicating if the progress of the algorithm should be traced (increasingly); default trace.lev = 0 does no tracing.
only.scale	logical indicating if only the scale of y should be computed. In this case, y will typically contain residuals.
mf	defunct.

Details

This function is used by lmrob.fit and typically not to be used on its own (because an S-estimator has too low efficiency ‘on its own’).

By default, the subsampling algorithm uses a customized LU decomposition which ensures a non singular subsample (if this is at all possible). This makes the Fast-S algorithm also feasible for categorical and mixed continuous-categorical data.

One can revert to the old subsampling scheme by setting the parameter subsampling in control to "simple".

Value

By default (when only.scale is false), a list with components

coefficients	numeric vector (length p) of S-regression coefficient estimates.
scale	the S-scale residual estimate
fitted.values	numeric vector (length n) of the fitted values.
residuals	numeric vector (length n) of the residuals.
rweights	numeric vector (length n) of the robustness weights.
k.iter	(maximal) number of refinement iterations used.
converged	logical indicating if all refinement iterations had converged.
control	the same list as the control argument.

If only.scale is true, the computed scale (a number) is returned.

Author(s)

Matias Salibian-Barrera and Manuel Koller; Martin Maechler for minor new options and more documentation.

See Also

lmrob, also for references.

Examples

set.seed(33)
x1 <- sort(rnorm(30)); x2 <- sort(rnorm(30)); x3 <- sort(rnorm(30))
X. <- cbind(x1, x2, x3)
y <-  10 + X. %*% (10*(2:4)) + rnorm(30)/10
y[1] <- 500   # a moderate outlier
X.[2,1] <- 20 # an X outlier
X1  <- cbind(1, X.)

(m.lm <- lm(y ~ X.))
set.seed(12)
m.lmS <- lmrob.S(x=X1, y=y,
                 control = lmrob.control(nRes = 20), trace.lev=1)
m.lmS[c("coefficients","scale")]
all.equal(unname(m.lmS$coef), 10 * (1:4), tolerance = 0.005)
stopifnot(all.equal(unname(m.lmS$coef), 10 * (1:4), tolerance = 0.005),
          all.equal(m.lmS$scale, 1/10, tolerance = 0.09))

## only.scale = TRUE:  Compute the S scale, given residuals;
s.lmS <- lmrob.S(X1, y=residuals(m.lmS), only.scale = TRUE,
                 control = lmrob.control(trace.lev = 3))
all.equal(s.lmS, m.lmS$scale) # close: 1.89e-6 [64b Lnx]

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