Re: [S] summary, df in smooths

Prof Brian D Ripley (
Thu, 1 Oct 1998 07:40:56 +0100 (BST)

On Thu, 1 Oct 1998, John Maindonald wrote:

> I'd be interested to get comments on whether an approach that seems to
> work well in tree-based regression might have application here also.
> I've been experimenting with the Atkinson & Therneau RPART library,
> which one can get from Statlib.
> They recommend marking any cv "error" ("risk") within one SE of the
> achieved minimum cv error as being equivalent to the minimum. Then
> the simplest model is chosen from among all those so tied. See

This `1-SE rule' goes back to at least Breiman, Friedman, Olshen & Stone
(1984), so there has been a lot of experience with it. Trees are a rather
particular problem, with lots of discrete choices, and fit criterion with
which this is used (the error rate) also has rather unusual properties.

Our experience in larger problems is that choosing any minimum (there can
be several) is usually better for prediction than the 1-SE rule, even in
the original context. For explanation, the 1-SE rule is a good idea.
However, with a different criterion (for example, for survival trees) the
1-SE rule does not work well even for explanation, choosing an excessively
simple tree.

Yes, the minimum for CV in smooth.spline can be very flat: more seriously
the curve of the cv-ed criterion can have multiple local minima a long way
apart. Curve smoothing problems can have more than one plausible degree of
smoothing adn which one prefers will depend on the purpose.

Brian D. Ripley,        
Professor of Applied Statistics,
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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