Claim·Untested·2605.00004

rem:thm-31

Under the setup above, the $L^{2}$ risk of $\hat{θ}_{2 S}$ satisfies $R_{2 S} (θ) \leq d σ^{2} - \frac{( d - 2 ) ^{2} σ ^{4}}{M + d σ ^{2}},$ with the inequality tight when $\overset{μ}{^}$ is a constant equal to $θ$ (where both sides reduce to $2 σ^{2}$ ).

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