AI 中文总结
该研究在局部渐近决策理论中，构建联合样本-菜单渐近理论，推导风险失真与均方误差阶，用校准菜单说明结果，以反例明确逐点高斯收敛的不足。
AI 中文摘要
我们研究局部渐近决策理论中的一个分辨率问题：个体风险可能存在高斯近似，但该近似无法确定其消失的差异。在上下文披露前设置有限个实验组成的菜单，尽管后续可自适应地对观测值进行路由。最大元Blackwell序将自适应路由简化为最优已设置实验，并将固定菜单的超额风险约化为带有前沿$A_k$的逆信息失真。我们沿一维退化链构建差异化的全先验后验转移，对每个具有正前沿的发散菜单序列及每个可容许的定位半径，无需额外的直接样本-菜单限制，即可建立$F_{n,k_n}(H_n)=A_{k_n}\{1+o(1)\}$。该转移在高斯退化下是精确的；无先验的似然生成器条件对跳跃生成器成立，且已在二元衰减、泊松 thinning、负二项 thinning 中得到验证。若失真在Ahlfors正则神谕像（维数为$r$）上是一致二次的，则$A_k\asymp k^{-2/r}$，原始尺度的超额均方误差阶为$n^{-1}k^{-2/r}$。校准后的泊松传感器与径向量子比特测量菜单可说明该结果；一个三角高斯反例表明逐点高斯收敛是不够的。
英文摘要
We study a resolution problem in local asymptotic decision theory: individual risks may admit Gaussian approximations that do not determine their vanishing difference. A finite menu of experiments is installed before context disclosure, although observations may be routed adaptively afterward. A greatest-element Blackwell order collapses adaptive routing to the best installed experiment and reduces the fixed-menu excess to an inverse-information distortion with frontier $A_k$. We develop differentiated, all-prior posterior transfer along a one-dimensional degradation chain and establish $F_{n,k_n}(H_n)=A_{k_n}\{1+o(1)\}$ for every diverging menu sequence with positive frontier and every admissible localization radius, without an additional direct sample-menu restriction. The transfer is exact under Gaussian degradation. Prior-free likelihood-generator conditions imply it for jump generators and are verified for binary attenuation, Poisson thinning, and negative-binomial thinning. If the distortion is uniformly quadratic on an Ahlfors-regular oracle image of dimension $r$, then $A_k\asymp k^{-2/r}$, and the original-scale excess mean squared error is of order $n^{-1}k^{-2/r}$. Calibrated Poisson sensor and radial-qubit measurement menus illustrate the result. A triangular Gaussian counterexample shows why pointwise Gaussian convergence is insufficient.
CommentsMain paper: 21 pages; supplementary material: 18 pages
