This is a general question on Robinson's equation which is a key element of generalised random forest (grf).
In the guided tour of grf package in r (https://grf-labs.github.io/grf/articles/grf_guide.html), it is mentioned that:
To solve the equation Y_i= f(x_i) + tau_i * W_i + e_i
"Robinson (1988) shows that this approach yields root-n consistent estimates of , even if estimates of () and () converge at a slower rate (“4-th root” in particular)"
"this approach" refers to the residual-on-residual regression, i.e. solving the "centred" equation of above using m(x) and e(x).
My question is that if I know that the data (x_i) cannot predict Y very well (poor discrimination and calibration from prior experience), then should that influence my confidence in estimating the treatment effect using grf technique? The guide did have a follow-up explanation that seems to suggest that even if m(x) is poorly estimated, consistent estimate of tau can still be derived. It feels like a leap of faith to accept this. Could someone please translate the quoted sentence into plain language, and point me towards a better understanding the "orthogonality" property?
Thank you!