R help - Oct 2003 - 2 D non-parametric density estimation

I have spatial data in 2 dimensions - say (x,y).  The correlation
between x and y is fairly substantial.  My goal is to use a
non-parametric approach to estimate the multivariate density describing
the spatial locations.  Ultimately, I would like to use this estimated
density to determine the area associated with a 95% probability contour
for the data.

Given the strong correlation between x and y, I have not been real
happy w/ the results obtained using kernel density estimators with
separate smoothing parameters for the x and y directions - e.g., bkde2D
(KernSmooth library), sm (sm library), kde2d (MASS library).   It seems
to me that a better alternative would be to transform the data to have
~0 correlation, estimate the density, then transform back to the
original scale.  Does this seem reasonable for this sort of problem? 
Has anyone written code in R to do this sort of thing?

I also attempted to explore local likelihood fitting (using locfit
library).  I liked the look of the estimated densities, but found it
difficult to obtain predictions at an arbitrary set of grid points (as
needed to determine a 95% probability contour).  Does anyone have
examples using locfit w/ the "ev" option or predict.locfit in order to
obtain local likelihood density estimates at an arbitrary set of grid
points?  

Any suggestions would be greatly appreciated!

John

John Fieberg, Ph.D.
Wildlife Biometrician, MN DNR
5463-C W. Broadway
Forest Lake, MN 55434
Phone: (651) 296-2704

John  -

My recollection is that Adrian Raftery's contributed package
'mclust'
does kernel density estimation as well.  Not sure whether it does what
you need.  Take a look at it on CRAN.  Ah..I see that the description
which shows up on Jon Baron's search page is not encouraging.  Give it
a try, anyway.  That description does not do it justice.

-  tom blackwell  -  u michigan medical school  -  ann arbor  -

On Wed, 22 Oct 2003, John Fieberg wrote:
> I have spatial data in 2 dimensions - say (x,y).  The correlation
> between x and y is fairly substantial.  My goal is to use a
> non-parametric approach to estimate the multivariate density describing
> the spatial locations.  Ultimately, I would like to use this estimated
> density to determine the area associated with a 95% probability contour
> for the data.
>
> Given the strong correlation between x and y, I have not been real
> happy w/ the results obtained using kernel density estimators with
> separate smoothing parameters for the x and y directions - e.g., bkde2D
> (KernSmooth library), sm (sm library), kde2d (MASS library).   It seems
> to me that a better alternative would be to transform the data to have
> ~0 correlation, estimate the density, then transform back to the
> original scale.  Does this seem reasonable for this sort of problem?
> Has anyone written code in R to do this sort of thing?
>
> I also attempted to explore local likelihood fitting (using locfit
> library).  I liked the look of the estimated densities, but found it
> difficult to obtain predictions at an arbitrary set of grid points (as
> needed to determine a 95% probability contour).  Does anyone have
> examples using locfit w/ the "ev" option or predict.locfit in
order to
> obtain local likelihood density estimates at an arbitrary set of grid
> points?
>
> Any suggestions would be greatly appreciated!
>
> John
>
> John Fieberg, Ph.D.
> Wildlife Biometrician, MN DNR
> 5463-C W. Broadway
> Forest Lake, MN 55434
> Phone: (651) 296-2704
>
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