robustbase (version 0.5-0-1)

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 = 0)

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.

Value

• A list with components
• coef
  numeric vector (length $p$) of S-regression coefficient estimates.
• scale
  the S-scale residual estimate
• cov
  covariance matrix ($p \times p$) of the coefficient estimates.
• 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.MM and not intended to be used on its own (because an S-estimator has too low efficiency on its own).

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("coef","scale")]
stopifnot(all.equal(m.lmS$coef,
                    10 * (1:4),        tol = 0.005),
          all.equal(m.lmS$scale, 1/10, tol = 0.09))