= Metric two-point risk bound
{title2=$R^*\ge\frac r2(1-\eta)(1-\mathbb E_0|Z-1|/\eta)$}
If two parameters are separated by at least $2r$ in a <metric>, any <estimator> gives a test by deciding whether its distance from the first parameter is below $r$. For $0<\eta<1$, the event $|Z-1|\le\eta$ and <Markov inequality> give the displayed <minimax risk> bound, where $Z$ is the product <likelihood ratio>. The unrestricted claim for every positive $\eta$ is false when both factors on the right are negative.
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