Cramér–Rao Bound
Fundamental lower limit on estimator variance from Fisher information
The Cramér–Rao bound states that for an unbiased estimator of parameter θ:
Var(estimator) ≥ 1 / I_F(θ)
where I_F is Fisher information. No amount of clever downstream processing can beat this limit — the bound is tight in the limit (e.g. maximum likelihood). A low-information sensor cannot be “fixed” by sophisticated L2 modelling; trustworthiness is ceilinged at observation.
Complements the data processing inequality (processing loses mutual information) with a measurement-theoretic floor on precision.
Corpus stance
A2 — working context: Formal support for “quality ceiling at observation”; see What Information Theory Says. (Cramér, 1946; Rao, 1945 — independent development of the inequality.)