Can someone provide me with a book or online reference on how to construct smoothing splines with cross-validation? I have a programming and undergraduate level mathematics background. I would also appreciate an overview of whether this is smoothing technique is a good one for smoothing data and whether there are any disadvantages of which a non-statistician needs to be aware.
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Nonparametric Regression and Spline Smoothing by Eubank is a good book. You probably want to start with Chapters 2 and 5 which cover goodness of fit and the theory and construction of smoothing splines. I've heard good things about Generalized Additive Models: An Introduction with R, which might be better if you're looking for examples in R. For a quick introduction, a google search turns up a course on Nonparametric function estimation where you can peruse the slides and see examples in R.
The general problem with splines is overfitting your data, but this is where cross validation comes in.
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$\begingroup$ Good references, but I don't understand your last comment about a parametric distribution. Splines are usually used for modelling the conditional mean of Y|X and are not directly to do with the distribution of either Y or X. I know you can fit spline-based density estimates, but I doubt that is what Henry was asking about. $\endgroup$ Aug 12, 2010 at 23:45
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$\begingroup$ Yes, the latter, but due to meandering and unrelated thoughts, not meant for "publication". I was thinking about density estimation because of some other question and, in light of this question, was working through explaining spline methods to myself. Strangely, I remember thinking what I typed was cogent -- because of what was in my head. Ridiculous. :-/ Thanks for the catch; impressed that it occurred to you, though I shouldn't be based on your quality answers. $\endgroup$– arsAug 13, 2010 at 2:44