These look like what are perhaps more commonly known
as (cubic) smoothing splines. They are implemented in
R, MATLAB, etc. What's quite nice for some purposes,
but not all, is that the knots are just all the distinct
x values, so there's no arbitrariness about that.
Well-banged on but old-fashioned Fortran is at Carl
de Boor's website in Wisconsin
http://www.cs.wisc.edu/~deboor/pgs
Nick
n.j.cox@durham.ac.uk
Maarten Buis replied to Adrian Mander
> Has anyone implemented a penalised cubic spline?
I tried some of that some time ago, and got stuck on the fact that
simple spline terms tend to become highly collinear and these penalized
splines typically require a large number of knots (and thus spline
terms). I could have tried figuring out how B-splines would have fitted
in a penalized spline function, but I didn't. However, an approach that
is similar can be found in (Royston and Sauerbrei 2007)
Patrick Royston and Willi Sauerbrei (2007) "Multivariate modeling with
cubic regression splines: A principled approach" The Stata Journal,
7(1), pp. 45-70.
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