Thank you
----- Original Message ----
From: spencerg <spencer.gra...@prodsyse.com>
To: "Liaw, Andy" <andy_l...@merck.com>
Cc: Rolf Turner <r.tur...@auckland.ac.nz>; FMH <kagba2...@yahoo.com>;
r-help@r-project.org
Sent: Wednesday, September 9, 2009 3:08:43 PM
Subject: Re: [R] Derivative of nonparametric curve
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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