From: Duncan Murdoch <murdoch_at_stats.uwo.ca>

Date: Wed 20 Jul 2005 - 05:58:48 EST

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

*>> > Hello,
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*>> >
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*>> > I have been trying to take the derivative of a quadratic B-spline
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*>> > obtained by using the COBS library. What I would like to do is
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*>> > similar to what one can do by using
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*>> >
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*>> > fit<-smooth.spline(cdf)
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*>> > xx<-seq(-10,10,.1)
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*>> > predict(fit, xx, deriv = 1)
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*>> >
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*>> > The goal is to fit the spline to data that is approximating a
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*>> > cumulative distribution function (e.g. in my example, cdf is a
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*>> > 2-column matrix with x values in column 1 and the estimate of the cdf
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*>> > evaluated at x in column 2) and then take the first derivative over a
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*>> > range of values to get density estimates.
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*>> >
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*>> > The reason I don't want to use smooth.spline is that there is no way
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*>> > to impose constraints (e.g. >=0, <=1, and monotonicity) as there is
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*>> > with COBS. However, since COBS doesn't have the 'deriv =' option, the
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*>> > only way I can think of doing it with COBS is to evaluate the
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*>> > derivatives numerically.
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*>>
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*>> Numerical estimates of the derivatives of a quadratic should be easy to
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*>> obtain accurately. For example, if the quadratic ax^2 + bx + c is
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*>> defined on [-1, 1], then the derivative 2ax + b, has 2a = f(1) - f(0) +
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*>> f(-1), and b = (f(1) - f(-1))/2.
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*>>
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*>> You should be able to generalize this to the case where the spline is
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*>> quadratic between knots k1 and k2 pretty easily.
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*>>
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*>> Duncan Murdoch
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*>>
*

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 06:01:32 2005

Date: Wed 20 Jul 2005 - 05:58:48 EST

On 7/19/2005 3:34 PM, James McDermott wrote:

> I wish it were that simple (perhaps it is and I am just not seeing > it). The output from cobs( ) includes the B-spline coefficients and > the knots. These coefficients are not the same as the a, b, and c > coefficients in a quadratic polynomial. Rather, they are the > coefficients of the quadratic B-spline representation of the fitted > curve. I need to evaluate a linear combination of basis functions and > it is not clear to me how to accomplish this easily. I was hoping to > find an alternative way of getting the derivatives.

I don't know COBS, but doesn't predict just evaluate the B-spline? The point of what I posted is that the particular basis doesn't matter if you can evaluate the quadratic at 3 points.

Duncan Murdoch

> > Jim McDermott > > On 7/19/05, Duncan Murdoch <murdoch@stats.uwo.ca> wrote:

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

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 06:01:32 2005

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