On knot placement for penalized spline regression

This paper studies the problem of knot placement in penalized regression spline fitting. Given a pre-specified number of knots, most existing knot placement methods allocate the knots in an equally spaced fashion. This paper proposes a simple knot placement scheme for improving such “equally spaced methods”. This new scheme first identifies locations of local extrema in the target function, and then it places additional knots in such places. The rationale behind this is that quite often such local extrema coincide with the critical locations for placing knots. The proposed scheme is shown to be superior in a simulation study.