Hi Christoph,
On a related tangent, you might be interested in a kernel regression
method. There are several versions of the 2-D Nadaraya-Watson algorithm
around (smooth.2d in the fields package, but I've never used that one).
It's a local average, and once you choose the exact function you use
(commonly a normal, but there are many other choices from cones to half
spheres to cauchys to ...). The main parameter of interest is the smoothing
parameter which controls local range of points (x_i,y_i) which influence the
regression value at some (x_0, y_0) This determines the flatness/peakedness
of the estimate. There is a similar issue with splines, usually they use a
penalty on the 2nd derivative (aka roughness penalty). I think Silverman
showed an equivalence between splines and kernel methods in the 1-d case.
Either way you have to face the question: what is the best smoothing
parameter for my data.
If you want to expand your choice of basis functions, the fda package has
some examples, but I haven't used it for 2-d smoothing.
Best,
Blair
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