[R] Kernel Density Estimation at manually specified points

[David Winsemius]

On Jun 27, 2011, at 3:18 PM, Carsten Harlaß wrote:

> Hello,
>
> thanks for your response.
>
> Of course I already thought about this "simple" solution of the  
> problem.
> But I think this is not a nice workaround.
>
> If I understand the manual correctly, density() already makes an
> approximation. But this approximation is just evaluated at the wrong  
> points.
>
> See:
>
> "Details
>
> The algorithm used in density.default disperses the mass of the
> empirical distribution function over a regular grid of at least 512
> points and then uses the fast Fourier transform to convolve this
> approximation with a discretized version of the kernel and then uses
> linear approximation to evaluate the density at the specified points."
>
> and
>
> "n 	the number of equally spaced points at which the density is to be
> estimated. When n > 512, it is rounded up to a power of 2 during the
> calculations (as fft is used) and the final result is interpolated by
> approx. So it almost always makes sense to specify n as a power of  
> two. "
>
> So this workaround means putting a second approximation on top of an
> other approximation. That's not nice. Or is it?

It's just a linear approximation between two points of the density$.  
If you need to you can make those point more numerous.  What  
alternative are you considering?

(I would also point out that approxfun may be even more helpful. It  
gives you the result as a function.)

-- 
David
>
> With kind regards
>
> Carsten
>
> Am 27.06.2011 19:16, schrieb David L Carlson:
>> Look at ?approx. For your example (of course your random numbers give
>> different results):
>>
>>> approx(f$x, f$y, c(-2, -1, 0, 1, 2))
>> $x
>> [1] -2 -1  0  1  2
>>
>> $y
>> [1] 0.03757113 0.19007982 0.31941779 0.37066592 0.10227509
>>
>> approx gives NA's if you try to interpolate outside the bounds of  
>> the data.
>> ----------------------------------------------
>> David L Carlson
>> Associate Professor of Anthropology
>> Texas A&M University
>> College Station, TX 77843-4352
>>
>>
>> -----Original Message-----
>> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org 
>> ] On
>> Behalf Of Carsten Harlaß
>> Sent: Sunday, June 26, 2011 7:02 PM
>> To: r-help at r-project.org
>> Subject: [R] Kernel Density Estimation at manually specified points
>>
>> Hello,
>>
>> my name is Carsten. This ist my first post to R-help mailing list.
>>
>> I estimate densities with the function "density" out of the package
>> "stats".
>>
>> A simplified example:
>>
>> 	
>> 	#generation of test data
>> 	n=10
>> 	z = rnorm(n)
>> 	
>> 	#density estimation
>> 	f=density(z,kernel="epanechnikov",n=n)
>>
>> 	#evaluation
>> 	print(f$y[5])
>>
>> Here I can only evaluate the estimation at given points. These points
>> are determined by the parameter n. By default they are equidistant
>> distributed on the interesting interval.
>>
>> But I need to evaluate the estimation (the estimated densitiy  
>> function)
>> at manually specified points. For example I want to compute f(z[i]).
>> This means I am interested in the estimated density at a the  
>> observation
>> z[i].
>>
>> Does anyone know how I can compute this? I think this is an ordinary
>> task so I would be surprised if R can not manage this. But even  
>> after a
>> long search I have found nothing.
>>
>> Thanks in advance
>>
>> Carsten Harlaß
>>
>> --
>> Carsten Harlaß
>> Aachen University of Applied Sciences
>> Campus Jülich
>> E-Mail: carsten_harlass at web.de
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
>> --
>> Carsten Harlass
>> Aachen University of Applied Sciences
>> Campus Juelich
>> E-Mail: carsten_harlass at web.de
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

David Winsemius, MD
West Hartford, CT