Fri Nov 14 22:16:28 CST 2008
On 14-Nov-08, at 6:26 PM, Anne Archibald wrote:
> The knots are specified in a form that allows them all to be treated
> identically. This sometimes means repeating knots or having zero
> If you have more data points than you want knots, then you are going
> to be producing a spline which does not pass through all the data. The
> smoothing splines include an automatic number-of-knots selector, which
> you may prefer to specifying the number of knots yourself. it chooses
> (approximately) the minimum number of knots needed to let the curve
> pass within one sigma of the data points, so by adjusting the
> smoothing parameter and the weights you can tune the number of knots.
> Evaluation time is not particularly sensitive to the number of knots
> (though of course memory usage is).
I see. I'm interested in doing is modeling the variation in the
curves, presumably via a description of the joint distribution of the
spline coefficients. This gets difficult if the number of knots is
variable, which is why I've gone this route. It's not important that
the curves fit the data exactly, but part of the reason for fitting
splines is to reduce each of many, many curves to a fixed-length
description. Does this make sense?
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