[R] Is it possible to separate two independent components from a random variable?

[Thomas Lumley]

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