loess documentation
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 α (set by span or enp.target). For α < 1, the neighbourhood includes proportion α of the points, and these have tricubic weighting (proportional to (1 - (dist/maxdist)^3)^3. For α > 1, all points are used, with the `maximum distance' assumed to be α 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 -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._