Hello,

I am using R and the smooth.Pspline function in the pspline package to
smooth some data by using natural cubic splines. After fitting a
sufficiently smooth spline using the following call:

(ps=smooth.Pspline(x,y,norder=2,spar=0.8,method=1)

[the values of x are age in years from 1 to 100]

I tried to check that R in fact had fitted a natural cubic spline by
checking that the resulting spline was LINEAR outside the knots. I did this
by plotting the predicted values from the spline fitting in the following
way:

plot(predict(ps,c(seq(100,150,1))

Unfortunately, the trend beyond the region of knots (i.e. over x values of
100) was far from linear - it was some sort of exponentially increasing
trend. My understanding of natural cubic splines (from Green and Silverman -
Nonparametric regression and generalized linear models, 1994) is that a
natural cubic spline is a series of cubic polynomials joined at a set of
knots in such a way that first and second derivatives are equal at all
knots. Furthermore, a natural cubic spline has a knot at every data point,
and is LINEAR on the range outside of its knots.

This leads me to the question of what smooth.Pspline actually performs to
the data and whether it actually fits a natural cubic spline as stated in
the help file? Or does smooth.Pspline work as I expect it, but I am using
predict incorrectly?

I thank you for your time.
Szymon

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