This may be overkill for your application, but you might be
interested in the "fda" package, for which a new book appeared a couple
of months ago: "Functional Data Analysis with R and Matlab" (Springer
Use R! series, by Ramsay, Hooker and Graves; I'm the third author).
The package includes a "scripts" subdirectory with R code to recreate
all but one of the 76 figures in the book. [To find this "scripts"
directory, use "system.file('scripts', package='fda')".]
Functional data analysis generalizes spline smoothing in two
important ways:
(1) It supports the use of an arbitrary finite basis set to
approximate elements of a function space; spline smoothing uses splines
only, usually cubic splines. The first derivative of a cubic spline is
piecewise quadratic, and the second derivative is piecewise linear. If
you want something smoother than linear, you need at least a quartic
spline, and Ramsay has recommended quintics -- degree 5 polynomials =
order 6 spline.
(2) It allows the curve to be smoothed using an arbitrary
linear differential operator, not just the second derivative. This can
be important if you have theory saying that the "truth" should follow a
particular differential equation. Otherwise, if you want to estimate
the second derivative, Ramsay has recommended smoothing with the fourth
derivative rather than the second. (In any event, smoothing is achieved
by penalized least squares with the penalty being proportional to the
integral of the square of the chosen linear differential operator.)
To reinforce this second point, chapter 11 of "Functional Data
Analysis with R and Matlab" describes "functional differential
analysis", which will estimate non-constant coefficients in a
differential equation model.
Hope this helps.
Spencer Graves
Liaw, Andy wrote:
From: Rolf Turner
On 8/09/2009, at 9:07 PM, FMH wrote:
Dear All,
I'm looking for a way on computing the derivative of first and
second order of a smoothing curve produced by a nonprametric
regression. For instance, if we run the R script below, a smooth
nonparametric regression curve is produced.
provide.data(trawl)
Zone92 <- (Year == 0 & Zone == 1)
Position <- cbind(Longitude - 143, Latitude)
dimnames(Position)[[2]][1] <- "Longitude - 143"
sm.regression(Longitude, Score1, method = "aicc", col = "red",
model = "linear")
Could someone please give some hints on the way to find the
derivative on the curve at some points ?
See
?smooth.spline
and
?predict.smooth.spline
Since sm.regression() (from the sm package, I presume) uses kernel
methods, a kernel-based estimator of derivatives is available in the
KernSmooth package.
Andy
cheers,
Rolf Turner
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--
Spencer Graves, PE, PhD
President and Chief Operating Officer
Structure Inspection and Monitoring, Inc.
751 Emerson Ct.
San José, CA 95126
ph: 408-655-4567
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