lmrob.fit {robustbase}

MM-type estimator for regression

Description

Compute MM-type estimators of regression: An S-estimator is used as starting value, and an M-estimator with fixed scale and redescending psi-function is used from there. Optionally a D-step (Design Adaptive Scale estimate) as well as a second M-step is calculated.

Usage

lmrob.fit(x, y, control, init = NULL, mf = NULL)

Arguments

x

design matrix (n \times p) typically including a column of 1s for the intercept.

y

numeric response vector (of length n).

control

a list of control parameters as returned by lmrob.control, used for both the initial S-estimate and the subsequent M- and D-estimates.

init

optional list of initial estimates. See Details.

mf

defunct.

Details

This function is the basic fitting function for MM-type estimation, called by lmrob and typically not to be used on its own.

If given, init must be a list of initial estimates containing at least the initial coefficients and scale as coefficients and scale. Otherwise it calls lmrob.S(..) and uses it as initial estimator.

Value

A list with components

fitted.values

X \beta, i.e., X %*% coefficients.

residuals

the raw residuals, y - fitted.values

rweights

robustness weights derived from the final M-estimator residuals (even when not converged).

rank

degree.freedom

n - rank

coefficients

estimated regression coefficient vector

scale

the robustly estimated error standard deviation

cov

variance-covariance matrix of coefficients, if the RWLS iterations have converged (and control$cov is not "none").

control

iter

converged

logical indicating if the RWLS iterations have converged.

init.S

the whole initial S-estimator result, including its own converged flag, see lmrob.S (only for MM-estimates).

init

A similar list that contains the results of intermediate estimates (not for MM-estimates).

Author(s)

Matias Salibian-Barrera, Martin Maechler and Manuel Koller

See Also

lmrob, lmrob..M..fit, lmrob..D..fit, lmrob.S