From: Duncan Murdoch <murdoch_at_stats.uwo.ca>

Date: Wed 20 Jul 2005 - 05:07:23 EST

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Wed Jul 20 05:12:33 2005

Date: Wed 20 Jul 2005 - 05:07:23 EST

On 7/19/2005 2:53 PM, James McDermott wrote:

> Hello,

*>
**> I have been trying to take the derivative of a quadratic B-spline
**> obtained by using the COBS library. What I would like to do is
**> similar to what one can do by using
**>
**> fit<-smooth.spline(cdf)
**> xx<-seq(-10,10,.1)
**> predict(fit, xx, deriv = 1)
**>
**> The goal is to fit the spline to data that is approximating a
**> cumulative distribution function (e.g. in my example, cdf is a
**> 2-column matrix with x values in column 1 and the estimate of the cdf
**> evaluated at x in column 2) and then take the first derivative over a
**> range of values to get density estimates.
**>
**> The reason I don't want to use smooth.spline is that there is no way
**> to impose constraints (e.g. >=0, <=1, and monotonicity) as there is
**> with COBS. However, since COBS doesn't have the 'deriv =' option, the
**> only way I can think of doing it with COBS is to evaluate the
**> derivatives numerically.
*

Numerical estimates of the derivatives of a quadratic should be easy to obtain accurately. For example, if the quadratic ax^2 + bx + c is defined on [-1, 1], then the derivative 2ax + b, has 2a = f(1) - f(0) + f(-1), and b = (f(1) - f(-1))/2.

You should be able to generalize this to the case where the spline is quadratic between knots k1 and k2 pretty easily.

Duncan Murdoch

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Wed Jul 20 05:12:33 2005

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