Luis,
See the fastICA package, in particular the final example in the function
fastICA's help page. This doesn't leave you with density estimates, but
with projection-pursuit directions; you still have to figure out how to fit
a density estimate to the rotated data. Actually, as I understand it,
XGobi also finds directions but does not fit a density. However, any
multivariate density estimator ought to be applicable. I'm not aware at
the moment of the tools R offers for multivariate density estimation, but
I'm sure there are multiple possibilities.
_The Elements of Statistical Learning_ by Hastie, Tibshirani, and Friedman
mention a "trick" to use classification tools (which model class
probabilities) to estimate density. Fundamentally, generate data from a
reference distribution, and use the classification tool to estimate
probability of observed data (as opposed to generated data) as a function
of the inputs. These probabilities, normalized to integrate to 1, form a
density estimate. Since there are so very many classification tools
available, this trick offers a lot of flexibility.
Good luck.
Jim Garrett
Baltimore, Maryland, USA
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