From: James McDermott <jp.mcdermott_at_gmail.com>

Date: Thu 21 Jul 2005 - 09:31:33 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 Thu Jul 21 09:42:03 2005

Date: Thu 21 Jul 2005 - 09:31:33 EST

Thanks a lot for the input on this Professor Murdoch. I really appreciate all the help.

Regards,

Jim

On 7/20/05, Duncan Murdoch <murdoch@stats.uwo.ca> wrote:

> James McDermott wrote:

*> > 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?
**>
**> Yes, if you restrict attention to an interval between knots. You'll
**> need to re-evaluate it for each such interval (but since quadratic
**> splines are continuous, you can reuse evaluations at the knots, and you
**> just need one new point in each interval).
**>
**> From a practical point of view, you need to make sure that COBS really
**> is giving you a quadratic spline and really is reporting all of the
**> knots correctly. Watch out for coincident knots (zero length
**> intervals); you don't care about the derivative on those, but they might
**> cause overflows in some calculations.
**>
**> Duncan Murdoch
**> >
**> > 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 Thu Jul 21 09:42:03 2005

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