@AryehKontorovich Any reference to the simpler setting?

@AryehKontorovich PS: I am not sure I understand what the paper does. I guess the result I am looking for is given by theorem 10 or corrolary 11. But the results are on $R_n(h,q)$, how do they transfer to $h$ (which is the equivalent of my $f$)?

@AryehKontorovich Thanks for you answer! Is there anything about the regressogram? I am surprised I cannot find anything in the literature (it is probably the simplest regression estimator), maybe I don't have the right keywords.