This page has a nice applet illustrating the concept of one-sided derivatives:
http://www.ies.co.jp/math/java/calc/limrl/limrl.html
On 3/23/08, Mohammed El Faramawi <[email protected]> wrote:
> Hi Kit,
> Thank you very much. Pardon me, I am not good in MAth.
> i will be very grateful if you explain more what you
> mean by "the derivative (slope) of the function is
> equal on either side of each knot point, but the
> curvature on either side may differ" and "The first
> and second derivatives of the function are equal on
> either side of each knot point." Thanks again Kit
>
>
> --- Kit Baum <[email protected]> wrote:
>
> > Mohammed said
> >
> > I have a question about cubic spline regression and
> > linear spline regressionv. I would like to know what
> > are the differences between them?
> >
> > From a mathematical standpoint a linear spline,
> > defined over a
> > number of 'knot points' (or join points) is
> > continuous but not
> > differentiable. It is the equivalent of a dot-to-dot
> > drawing from
> > kindergarten.
> >
> > A quadratic spline is continuous and once
> > differentiable. That is,
> > the derivative (slope) of the function is equal on
> > either side of
> > each knot point, but the curvature on either side
> > may differ.
> >
> > A cubic spline is continuous and twice
> > differentiable. The first and
> > second derivatives of the function are equal on
> > either side of each
> > knot point.
> >
> > A polynomial spline of order k is differentiable
> > (k-1) times.
> >
> > There are different kinds of splines; e.g. b-splines
> > that have
> > similar properties, but are defined using different
> > mathematics than
> > polynomial splines.
> >
> > Linear splines are discussed in my book, referenced
> > below.
> >
> > Kit
> >
> > Kit Baum, Boston College Economics and DIW Berlin
> > http://ideas.repec.org/e/pba1.html
> > An Introduction to Modern Econometrics Using Stata:
> > http://www.stata-press.com/books/imeus.html
> >
> >
> > *
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> > *
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> > * http://www.ats.ucla.edu/stat/stata/
> >
>
>
>
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