eigen analysis : how to recompose the signal?

Hello,

Let's imagine I am using an eigen analysis to decompose n variables observed
p times. This will produce a subset of c components, c<<n, explaining most
of the signal : a vector of [c] eigenvalues, a matrix of [n,c] loadings and
a matrix of [p,c] scores.

Now, I would like to use only the variables having the greatest loadings in
order to estimate what the 'real' observation would be. How do I recompose
the signal ? How can I better characterize this estimatation (e.g.
confidence interval) ?

Is it something like :
observation = sum(1 to c)
[sqrt(eigenvalue(c)).loading(variable,c).measure(variable)]

Thanks

Olivier.



.

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