From: James McDermott <jp.mcdermott_at_gmail.com>

Date: Wed 20 Jul 2005 - 11:50:15 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 11:59:36 2005

Date: Wed 20 Jul 2005 - 11:50:15 EST

Would the unique quadratic defined by the three points be the same curve as the curve predicted by a quadratic B-spline (fit to all of the data) through those same three points?

Jim

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

> 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:
**> >> > 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
**> >>
**>
**>
*

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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 11:59:36 2005

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