[R] Plotting Bivariate Normal Data

[Liaw, Andy]

> From: Berton Gunter
>  
> 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"?) 

How about `long skirt' or some such?  That seems descriptive, at least for
2D...

Andy

> 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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