Talk:Chapman–Robbins bound

Question: Is it important that θ ∈ Rⁿ or it can be in arbitrary set ?

Answer: As far as I can tell, the proof works for arbitrary $\Theta$. But in order to be used for estimation theory, to make ${\hat {g}}$ an estimator for $\theta$, ${\hat {g}}$ has to be $\Theta$-valued. And since ${\hat {g}}$ is $\mathbb {R} ^{m}$-valued in the theorem, it's better be $\Theta \subseteq \mathbb {R} ^{m}$ in that context. — Preceding unsigned comment added by 77.179.139.65 (talk) 05:13, 9 August 2023 (UTC)