robustbase (version 0.92-5)

lmrob.S: 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, mf = NULL)

Arguments

x

design matrix

y

response vector

control

list as returned by lmrob.control

trace.lev

integer indicating if the progress of the algorithm should be traced (increasingly); default trace.lev = 0 does no tracing.

mf

(optional) a model frame as returned by model.frame, used only to compute outlier statistics, see outlierStats.

Value

• 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.

Details

This function is used by lmrob.fit and not intended 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".

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))