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Re: confidence ellipses

To: Pedram Sendi <psendi@uhbs.ch>
Subject: Re: confidence ellipses
From: Prof Brian D Ripley <ripley@stats.ox.ac.uk>
Date: Tue, 16 Sep 2003 09:44:12 +0100 (GMT Day
Cc: s-news@lists.biostat.wustl.edu
In-reply-to: <2003916221849.231814@ws508117>
On Tue, 16 Sep 2003, Pedram Sendi wrote:

> I have approximated a bivariate distribution f(a,b) using simulation, i.e.
> I have 5000 values of pairs of a,b. I would now like to plot a smooth 95%
> confidence ellipse, 50% confidence ellipse and 5% confidence ellipse. The
> contour plot feature does not seem to work. I would be very grateful if
> someone could tell me how to accomplish this in S-Plus 6.1 for Windows.

So you approximated a density by 5000 point values?  That's not a very good
approximation!  What makes you think that there is a confidence ellipse (as
distinct from any other shape of region)?  And do you mean a confidence
region, which needs a parametrized model?

What I can help with is finding a contour plot of the underlying density.
First find a 2d density estimate (using e.g. kde2d in MASS or the functions
in KernSmooth), and compute the density values of your 5000 points, and
sort them.  Then the 5%, 50% and 95% quantiles of those density values can
be used as contour levels for a plot of the density estimate (evaluated at
a rectangular grid).  That's the best interpretation I can find of your
intentions.  You will find relevant examples in MASS (the book).

An alternative interpretation would be to assume a bivariate normal or t
distribution (which have elliptical contours), fit that and then plot the
appropriate density contours.

-- 
Brian D. Ripley,                  ripley@stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595



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