[R] Results of MCD estimators in MASS and rrcov

[Valentin Todorov]

The two implementations use different consistency factors as well as
different small sample correction factors.

1. The search parts of both implementations produce the same result -
compare rrcov.mcd$best and mass.mcd$best.

2. The raw MCD covariance matrix is corrected as follows:

MASS:
 - Rousseeuw and Leroy (1987), p.259 (eq. 1.26)
 - Marazzi (1993) (or may be Rousseeuw and van Zomeren (1900) p.638 (eq A.9)

rrcov:
 - Croux and Haesbroeck (1999), Pison et.al. p. 337
 - Pison et.al. (2002), p.338

3. The reweighted (final) covariance matrix is corrected as follows:

MASS: no correction
rrcov: Pison et.al. (2002) p. 339

This explains the different covariance matrices.
As far as the location is concerned, in this particular case the raw MCD
estimates in MASS identify one additional outlier - observation 53, which is
discarded from the computation of the reweighted estimates.
Look at the following plots and judge yourself if this is an outlier or not:

  covPlot(hbk, mcd=rrcov.mcd, which="distance", id.n=15)
  covPlot(hbk, mcd=mass.mcd, which="distance", id.n=15)

valentin