Say I have 3 random variables ${X, Y, Z}$, and I have collected an iid sample of size $N$ from them: ${\cal D} = \{ (x_i, y_i, z_i), i = 1,\dots,N \}$. The conditional expectation $E[ X | y ]$ can also be written as
\begin{eqnarray*} E[ X | y ] = \int E[ X | y, z ] \,\, dF_{ Z | Y }(z) \end{eqnarray*}
My objective is to learn $E[ X | y ]$ from ${\cal D}$, and my question is: For finite sample size, should I expect any numerical advantage from learning $ E[ X | y, z ], dF_{ Z | Y }(z)$ first, and then integrating out the dependence on z? Or, can I discard the data collected about $z$, and directly learn $E[ X | y ]$.
To make things simpler, I'm ready to assume that my learning strategy is consistent.