= Gaussian location minimax lower bound under absolute-error loss
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{title2=$\sup_\mu\mathbb E_\mu|T-\mu|\geq\sigma/(4\sqrt{2n})$}
For $n$ <independent> observations with a <normal distribution> $N(\mu,\sigma^2)$, $\sigma>0$ fixed, every <estimator> has $\sup_\mu\mathbb E_\mu|T-\mu|\geq\sigma/(4\sqrt{2n})$. Compare $\mu_0=0$ and $\mu_1=\sigma/\sqrt{2n}$: the joint <Kullback-Leibler divergence> is $1/4$, so the <total variation–Hellinger–relative entropy inequality> bounds <total variation distance> by $1/2$. Apply the <Le Cam lower bound under absolute-error loss>. Degenerate zero-noise laws do not satisfy a positive lower bound.
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