Re: [S] comparing spline fits with different df?

Bill Shipley (
Wed, 8 Apr 1998 15:47:46 -0400

Bill Shipley wrote:
> Hello,
> I know that there are a number of different methods that have been suggested
> to choose the "best" span value, or smoother df, when using spline
> smoothers. However, I would like to know if there is any way of testing
> whether or not a spline fit with x df provides a significantly better fit
> than a spline fit with y df? In other words, assuming normality and
> homogeneity of variance for the residuals, what is the sampling distribution
> of the smoother cross-validation score?

Brian Ripley responded:

None I would trust very much. If the asymptotic theory is applicable,
you could just use AIC to compare them, that is

AIC = n log (RSS/n) + 2 * df.

Only use this for df small compared with n, though.

How about this: take a large number of bootstrap samples and fit with x df
to get the empirical distribution of cv. Now see if the cv obtained with y
df in the original sample falls in the lower 95% of this bootstrap
distribution. If not, then y df gives a significantly larger cv score.
Bill Shipley
Departement de Biologie
Universite de Sherbrooke
Sherbrooke (Quebec)
voix: 819-821-8000 poste 2079
telecopieur: 819-821-8049
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