# Tag Info

Adding to the excellent answer by @Alecos Papadopoulos, here are two simple numerical examples with $z=x^2+v$, $z^*$ is mean-centred $z$ and $v$ is independent from $u$, in which $E(xu)\neq 0$, $E(xz^*)\neq 0$, but $E(z^*u)=0$. Example 1 (with $x$ having a symmetric distribution) $E(xu)=1.5$, $E(xz^*)=-0.5$, $E(z^*u)=0$ Example 2 (showing that the ...