[R] Plotting Bivariate Normal Data

Berton Gunter gunter.berton at gene.com
Mon Oct 25 20:31:00 CEST 2004

Just a little addendum to Martin's comments below. It is well known that
using LS centers and covariances for the M-distances is generally not a good
way to do this, as these statistics, themselves, are distorted by the long
"tails" (do > 1D distributions have "tails"?)  so that the problems are
hidden (see Brian Ripley's comments on the R-Help "robust regression with
groups" thread  from last week). Hence, one should use a resistant center
(the medioid, say) and a resistant covariance matrix (e.g., from cov.rob())
to compute the M-distances.

... But then, this begs the question: Why do normality testing at all?
(again, see BR's comments). Better to use robust/resistant statistical
procedures for estimation from the beginning, though, unfortunately, this
shatters the nice simple mathematical framework for inference. 

-- Bert Gunter
Genentech Non-Clinical Statistics
South San Francisco, CA
"The business of the statistician is to catalyze the scientific learning
process."  - George E. P. Box

> Since one of the more severe and common deviations from
> normality is "long tailed"ness (in all it's vaguety), we have
> been recommending to QQ-plot mahalanobis distances against chi
> squared quantiles - even before looking at the univariate
> QQ plots.
> Exactly for this reason, in R,
> 	example(mahalanobis)
> shows a version of how to do this!
> Martin Maechler, ETH Zurich
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