Thanks a lot for the input on this Professor Murdoch. I really appreciate all the help.
Regards, Jim On 7/20/05, Duncan Murdoch <[EMAIL PROTECTED]> 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 <[EMAIL PROTECTED]> 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 <[EMAIL PROTECTED]> 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 > >>>> > >> > >> > > ______________________________________________ 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