Hi,
I encountered a problem in which I don't know whether I should
do a conditional or unconditional expectation on a random variable. Any
advice will be appreciated.
A simplified regression problem is formulated as the follows.
y(i) = x(i) b + e(i) = x(i) b + (u(i) + v(i))
where e=(u+v) are the composite error,
u(i) ~ N(mu(i), 1),
v(i) ~ N(0, 1).
The estimation is carried out using maximum likelihood estimation. Now,
I
want to do predictions on u(i). I can do either E(u(i)) (unconditional
expectation) or E(u(i) | e_(i)) (expectation conditional on the
estimated
composite error). I think if the empirical data is not the whole
population, conditional expectation may be more appropriate; is this
correct? Anyway, I'd like to know what is the advantage of doing one
over
another, and/or in what situation should I choose one over another.
Many thanks.
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