R help - Aug 2003 - Is it possible to separate two independent components from a random variable?

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)?

Maybe there is no way to figure it out, and just
wanna get some help and try it.

Fred

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