[R] Bounded Density Estimation

Alexander A. Morgan amorgan at linus.mitre.org
Fri Dec 8 19:28:08 CET 2000

	I have been using R and the locfit package for Unix/Linux for a
little while.  However, I have had some trouble, as I am trying to do
density estimation for bounded independent variables.  There is some
discussion in the density estimation book by Azzalini, but none in the
book by C Loader (creator of locfit).     Also, the variables that I am
working on are bounded on both sides, not just on the left (ie constrained
to be positive).  I have tried the following transformation:

log(x-minval) - log(maxval-x) = x' but with no good results.

Is there a way to use variable kernels or bandwidths to address this?  As
a test case, I was looking at a square of random points (ie even random
distribution), hoping to get a flat density estimation.  As expected, it
drops down at the edges, and precipitously at the corners.

I also tried going into the locfit code to see how I could make kernel
changes, and was sort of daunted by the layers of switch statements and
largely undocumented code.   I am still rather perplexed by the role of
'degree' as a locfit argument.  It makes sense in a local regression, but
doesn't seem to make sense in a nonparameteric density estimation (only
bandwith and kernel seem approriate).  However, degree seems to be related
to the smoothness of the fit, just as in regression.

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