[R] Is it possible to separate two independent components from a random variable?
Thomas Lumley
tlumley at u.washington.edu
Fri Aug 15 19:48:20 CEST 2003
On Fri, 15 Aug 2003, Feng Zhang wrote:
> Hey, R-listers,
>
> Given the observed N random scalar variable x, with
> zero mean and unit variance, can we separate the
> two independent component x1 and x2 such that
> x = x1 + x2 (x1 and x2 are assumed to be zero mean)?
>
Not without further information or constraints.
For example
- if x is Normal then x1 and x2 must be Normal but their
variances can be anything that add to 1
- if one distribution is known completely the other can be found
- If x1 and x2 are unimodal and x is bimodal you can find at least
something about x1 and x2.
This last one is a type of cluster analysis.
-thomas
Thomas Lumley Assoc. Professor, Biostatistics
tlumley at u.washington.edu University of Washington, Seattle
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