S-regression estimators

Description

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

Usage

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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.

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".

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.

Author(s)

Matias Salibian-Barrera and Manuel Koller (and Martin Maechler for minor details)

See Also

lmrob, also for references.

Examples

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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))

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