[R] Results of MCD estimators in MASS and rrcov

[rainer grohmann]

Thanks a lot!

Indeed, both implementations agree on the 'best' points. Your answer helped
me a great deal.

Rainer

> 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
> 

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