I'm attempting to derive an influence curve. I'm not necessarily looking for an answer, but guidance on how to tackle something that should be relatively straightforward (I think). I'm asked the following:
Rewrite the parameter mapping $\Psi^1(P) = E[E[Y | A=1, W] | A=0]$ so that you have $P(A=0) $ in the denominator and an integral expression in the numerator.
I'm thrown off by the embedded conditional expectation within conditional expectation. What might be relevant are the following:
$(W,A,Y) \sim P \in M $
$W=$ Vector of covariates
$A,Y =$ binary $(0,1)$
My initial guess was :
$\frac{\int f(W=w, A=1, Y=y)}{P(A=0)}$
Though, this seems forced