R help - Dec 2005 - bivariate kernel density estimates at point locations (rather than at grid locations)

Hi,

My data consists of a set of point locations (x,y). 

I would like to know if there is a procedure for bivariate kernel
density estimation in R that returns the density estimates at the
observed point locations rather than at grid locations. I have looked at
a number of different routines and they all seem to return estimates at
grid locations.  

Any type of kernel is fine (i.e., Gaussian, Quartic, etc).  

Thank you for your help!

Matt Strickland
U.S. Centers for Disease Control and Prevention

On Thu, 15 Dec 2005 14:21:17 -0500, Strickland, Matthew wrote:

SM> Hi,
SM> 
SM> My data consists of a set of point locations (x,y). 
SM> 
SM> I would like to know if there is a procedure for bivariate kernel
SM> density estimation in R that returns the density estimates at the
SM> observed point locations rather than at grid locations. I have
SM> looked at a number of different routines and they all seem to
SM> return estimates at grid locations.  
SM> 

One option is to use (from package sm), 
  sm.density(xy, eval.points=xy, eval.grid=FALSE)
where xy in a (n\times 2) matrix.

Best wishes,
Adelchi Azzalini

-- 
Adelchi Azzalini  <azzalini at stat.unipd.it>
Dipart.Scienze Statistiche, Universit?? di Padova, Italia
tel. +39 049 8274147,  http://azzalini.stat.unipd.it/

Hello Dr. Adelchi Azzalini,

Thank you for your quick response to my question that I posted on the r-help
board about bivariate kernel density estimates.  I have been using your sm
package the past few days and have encountered a problem with estimating the
density for only 1 point. I am using R 2.2.0, sm version 2.1-0 on a Windows
machine.  Example code below:

#The code below creates 3 point locations

x.locs = c(74, 75, 77)
y.locs = c(64, 63, 61)
points = cbind(x.locs, y.locs)

#If I send this data into sm.density everything works fine.

dens = sm.density(points, h=c(1, 1))

#However, if I only wish to send 1 point location to sm.density, i.e.,

points.2 =points[1,]
dens.2 = sm.density(points.2, h=c(1, 1)) 

R returns to me the error:length(h) != 1

It appears to me that sm.density thinks that my 1 point is a 1-dimensional
location rather than a 2-dimensional location, and I am getting an error when I
request a bivariate kernel.  Do you have any suggestions?

Best,
Matt


-----Original Message-----
From: Adelchi Azzalini [mailto:azzalini at stat.unipd.it] 
Sent: Friday, December 16, 2005 2:42 AM
To: Strickland, Matthew
Cc: r-help at stat.math.ethz.ch; adrian at stats.gla.ac.uk
Subject: Re: [R] bivariate kernel density estimates at point locations (rather
than at grid locations)

On Thu, 15 Dec 2005 14:21:17 -0500, Strickland, Matthew wrote:

SM> Hi,
SM> 
SM> My data consists of a set of point locations (x,y). 
SM> 
SM> I would like to know if there is a procedure for bivariate kernel 
SM> density estimation in R that returns the density estimates at the 
SM> observed point locations rather than at grid locations. I have 
SM> looked at a number of different routines and they all seem to return 
SM> estimates at grid locations.
SM> 

One option is to use (from package sm),
  sm.density(xy, eval.points=xy, eval.grid=FALSE) where xy in a (n\times 2)
matrix.

Best wishes,
Adelchi Azzalini

--
Adelchi Azzalini  <azzalini at stat.unipd.it> Dipart.Scienze Statistiche,
Universit?? di Padova, Italia tel. +39 049 8274147, 
http://azzalini.stat.unipd.it/

On Wed, 21 Dec 2005 12:21:54 -0500, Strickland, Matthew wrote:

SM> Hello Dr. Adelchi Azzalini,
SM> 


Dr. Strickland, 

your message was directed to the whole r-help list with no CC to
myself, and sometimes I do not have the chance to browse the
 r-help list for weeks..

SM> Thank you for your quick response to my question that I posted on
SM> the r-help board about bivariate kernel density estimates.  I have
SM> been using your sm package the past few days and have encountered
SM> a problem with estimating the density for only 1 point. I am using
SM> R 2.2.0, sm version 2.1-0 on a Windows machine.  Example code
SM> below:
SM> 
SM> #The code below creates 3 point locations
SM> 
SM> x.locs = c(74, 75, 77)
SM> y.locs = c(64, 63, 61)
SM> points = cbind(x.locs, y.locs)
SM> 
SM> #If I send this data into sm.density everything works fine.
SM> 
SM> dens = sm.density(points, h=c(1, 1))
SM> 
SM> #However, if I only wish to send 1 point location to sm.density,
SM> #i.e.,
SM> 
SM> points.2 =points[1,]
SM> dens.2 = sm.density(points.2, h=c(1, 1)) 
SM> 
SM> R returns to me the error:length(h) != 1

formally, the error is due to this

R> is.vector(points.2)
[1] TRUE

sm.density receives a vector of length 2, and it  works for that
case: estimation of a one-dimensional density from which you
supplied two data values. Then it finds a two-dimensional h
and there it complains.

On the statistical side, I cannot follow the logic of estimating
nonparametrically a density function on the basis of only one 
(supposed bivariate) observation.

SM> 
SM> It appears to me that sm.density thinks that my 1 point is a
SM> 1-dimensional location rather than a 2-dimensional location, and I
SM> am getting an error when I request a bivariate kernel.  Do you
SM> have any suggestions?  
SM> 

I am not sure to grasp what you have in mind; is it perhaps that you
want the following?

dens.2 = sm.density(points, h=c(1, 1), eval.points=points, eval.grid=FALSE) 
print(dens.2$estimate[1])

best regards,

Adelchi


SM> Best,
SM> Matt
SM> 
SM> 
SM> -----Original Message-----
SM> From: Adelchi Azzalini [mailto:azzalini at stat.unipd.it] 
SM> Sent: Friday, December 16, 2005 2:42 AM
SM> To: Strickland, Matthew
SM> Cc: r-help at stat.math.ethz.ch; adrian at stats.gla.ac.uk
SM> Subject: Re: [R] bivariate kernel density estimates at point
SM> locations (rather than at grid locations)
SM> 
SM> On Thu, 15 Dec 2005 14:21:17 -0500, Strickland, Matthew wrote:
SM> 
SM> SM> Hi,
SM> SM> 
SM> SM> My data consists of a set of point locations (x,y). 
SM> SM> 
SM> SM> I would like to know if there is a procedure for bivariate
SM> SM> kernel  density estimation in R that returns the density
SM> SM> estimates at the  observed point locations rather than at grid
SM> SM> locations. I have  looked at a number of different routines
SM> SM> and they all seem to return  estimates at grid locations.
SM> SM> 
SM> 
SM> One option is to use (from package sm),
SM>   sm.density(xy, eval.points=xy, eval.grid=FALSE) where xy in a
SM>   (n\times 2) matrix.
SM> 
SM> Best wishes,
SM> Adelchi Azzalini
SM> 
SM> --
SM> Adelchi Azzalini  <azzalini at stat.unipd.it> Dipart.Scienze
SM> Statistiche, Universit?? di Padova, Italia tel. +39 049 8274147, 
SM> http://azzalini.stat.unipd.it/
SM> 
SM> ______________________________________________
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SM> PLEASE do read the posting guide!
SM> http://www.R-project.org/posting-guide.html
SM>