[R] loess documentation

[Prof Brian D Ripley]

On Wed, 15 Nov 2000, Derrick P. Snowden wrote:

> Hi all,
> 
> I 've got a question about the usage of loess in the modreg package. 
> The documentation (loess.html) states that the smoothing window is
> either set by span or enp.target.  If span is used,  the details section
> of the docs state...
> 
> <SNIP>
> 
> DETAILS
> 
> Fitting is done locally. That is, for the fit at point x, the fit is
> made using points in a neighbourhood of x, weighted by their distance
> from x (with differences in `parametric' variables being ignored when
> computing the distance). The size of the neighbourhood is controlled by
> &alpha; (set by span or enp.target). 
> 
> For &alpha; < 1, the neighbourhood includes proportion &alpha; of the
> points, and these have tricubic weighting (proportional to (1 -
> (dist/maxdist)^3)^3. 
> 
> For &alpha; > 1, all points are used, with the `maximum distance'
> assumed to be &alpha; times the actual maximum distance. 
> 
> </SNIP>
> 
> I understand the situation when alpha is less than one, presuming it
> uses the same convention set forth in any number of Clevelend and Devlin
> articles, ie, nearest neighbor smoothing.  
> 
> However, I'm interested in looking at fixed bandwidth smoothing and I'm
> wondering if the second option, (alpha>1) is some variation of this
> theme.  I don't understand the "alpha times actual maxdistance"
> statement.  If my estimation point is 10 meters from the farthest data
> point in physical space and I set my alpha = 2, then according to the
> statement above the smoothing window would be 20m????  Obviously this
> can't be right.  Where have I gone wrong?

Yes it can be right. Read those Cleveland et al articles again. See for
example the White Book page 315. It's a weighted average over the
window, so still sensible for a bigger window.

Actually, I think it might be alpha^(1/p), but the docs are unclear on
that.

-- 
Brian D. Ripley,                  ripley at 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 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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