R: S-regression estimators

lmrob.S {robustbase} | R Documentation

## S-regression estimators

### Description

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

### Usage

    lmrob.S(x, y, control,
            trace.lev = control$trace.lev,
            only.scale = FALSE, mf = NULL)

### Arguments

`x` | design matrix (n * p)
`y` | numeric vector of responses (or residuals for `only.scale=TRUE`).
`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.
`only.scale` | `logical` indicating if only the scale of `y` should be computed. In this case, `y` will typically contain residuals.

`mf` | unused and deprecated.

### Details

This function is used by `lmrob.fit` and typically not 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

By default (when `only.scale` is false), 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.

If `only.scale` is true, the computed scale (a number) is returned.

### Author(s)

Matias Salibian-Barrera and Manuel Koller; Martin Maechler for minor new options and more documentation.

### 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("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))

    ## only.scale = TRUE:  Compute the S scale, given residuals;
    s.lmS <- lmrob.S(X1, y=residuals(m.lmS), only.scale = TRUE,
                     control = lmrob.control(trace.lev = 3))
    all.equal(s.lmS, m.lmS$scale) # close: 1.89e-6 [64b Lnx]

[Package robustbase version 0.93-6 Index]