R help

Peter Dalgaard writes:

Shutnik <shutnik_xx at yahoo.co.uk> writes:

 Hello,
 I have the normal random variables y(t)~N(mu, sigma.sq) and want
 to decompose them into n normal variables:

 y(t) = x(t,1) + 

+ x(t,n) 

	I presume this means y(t) = x(t,1) + ... + x(t,n)  (R.T.)

x(t,i)~N(mu, sigma.sq/n) 

I presume you want x(t,i)~N(mu/n, sigma.sq/n),
	elsewise the question doesn't make sense.

	I also presume you want the x(t,i) to be independent,
	elsewise the question is trivial.                  (R.T.)

 The problem is not as simple as can appear. All my experiments
 didnt give me anything so far. Are there any tools to do this?

This should work, provided I understand the problem correctly:

x <- rnorm(n,sd=sqrt(sigma.sq/n))
x <- x - mean(x) + y/n

I don't think it's that simple:  By my calculations,

	Var(x_i) = 2*sigma.sq/n - sigma.sq/n^2,  not sigma.sq/n.

I think the problem is actually fairly subtle (although I may
be overlooking something simple).  Something like a Gramm-Schmidt
approach should work, but I can't quite suss it out.

					cheers,

						Rolf Turner
						rolf at math.unb.ca