Good point! More precisely, an arbitrary estimator Q may have significant error w.r.t.E[Q(x)] because Var[Q(x)] doesn’t have to be small but it doesn’t matter because we can always amplify Q by running it multiple times and averaging the results. So we still get a hierarchy, just slightly less tight (but this tightness is not very interesting since it depends on the computational model anyway).
Good point! More precisely, an arbitrary estimator Q may have significant error w.r.t.E[Q(x)] because Var[Q(x)] doesn’t have to be small but it doesn’t matter because we can always amplify Q by running it multiple times and averaging the results. So we still get a hierarchy, just slightly less tight (but this tightness is not very interesting since it depends on the computational model anyway).