# 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 x p) typically including a column of `1`s 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` unused and deprecated.

### 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`