# lmrob.fit: MM-type estimator for regression In robustbase: Basic Robust Statistics

 lmrob.fit R Documentation

## 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

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