[AniMov] href bandwidths

John Fieberg John.Fieberg at dnr.state.mn.us
Thu Jul 5 17:54:16 CEST 2007


Hi Clément, 

I may be able to help clear up a little bit of the confusion regarding
the differences in href bandwidth recommendations (i.e., related to your
earlier inquiry below):

"Silverman recommends a value of href equal to h = 1.06*sigma*n^-1/5,
whereas Worton recommends sigma*n^-1/6. Actually, I do not know the
reason for the difference between the href of worton and the href of
Silverman... The recommendation of Silverman is probably more justified,
and you're probably right, it may be a good idea to provide a default
value for the smoothing parameter which gives a better estimate.  I will
change the default value of href accordingly for the next version of
adehabitat."

Both of these suggestions assume the underlying data are Gaussian, but
Silverman's recommendation (n^-1/5) is optimal for estimating the
density in the univariate case, whereas Worton's (n^-1/6) is optimal for
bivariate data [in general, the optimal h for density estimation is
proportional to n^-1/(d+4)].  Importantly, the bandwidth that is optimal
for estimating the *density* (or UD) may not be optimal for estimating
home range (HR) size (e.g., using the 95% probability contour). 

For univariate Gaussian data, the optimal bandwidth for estimating the
cumulative distribution function is proportional to n(^-1/3) rather than
n^(-1/5). Since HR size is calculated using the cumulative distribution
function rather than the density, I would not be surprised if a smaller
bandwidth (than n^-1/6) turned out to be more optimal for estimating HR
size.

Hope this is helpful.

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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