无尺度形状：通过非加性测量核观测的有界尾部的一个可辨识性二分法
Shape without scale: an identifiability dichotomy for a bounded tail observed through a non-additive measurement kernel
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中文总结 AI 辅助
该研究针对有界尾部经非加性测量核观测的可辨识性问题，证明形状参数可辨识而速率参数不可辨识，并给出速率需锚点的充分条件，应用于替代安全性分析。
中文摘要 AI 辅助
一个潜在严重性具有有界下尾，其密度形状为alpha，尺度为L。它仅通过一个固定的、有偏且非加性的马尔可夫核K被观测。K的相对条件扩散在端点处发散。我们的样本仅来自边际分布Q的独立同分布，没有锚定协变量或工具。我们证明了一个二分法。形状指数alpha是可辨识的：对于类常数的每个可接受选择，一个精简类中的任意两个观测等价成员共享alpha，该alpha由Q的近端点展开决定。速率，即L和固定尺度超阈值p_tau，无法保留。存在可接受的共享类常数和较小正则类中的两个成员，其观测定律完全一致。在这对成员中，alpha一致，而L和p_tau发生变化。一个退化的Le Cam两点界排除了对任一参数的任何一致估计量，且逐点一致性在一个成员处失败。只有速率需要锚点。我们推测，一个具有已知边缘映射的已知核族，当且仅当该族满足固定尺度单射性条款时，才能逐纤维地识别速率，并且我们证明了充分性方向。在替代安全性中，未校准的冲突数据给出了近碰撞风险形状，而非其绝对速率。
英文摘要
A latent severity has a bounded lower tail with density of shape alpha and scale L. It is observed only through a fixed Markov kernel K that is biased and non-additive. The relative conditional spread of K diverges at the endpoint. Our sample is i.i.d. from the marginal Q alone, with no anchoring covariate or instrument. We prove a dichotomy. The shape index alpha is identifiable: for every admissible choice of the class constants, any two observationally equivalent members of a lean class share alpha, determined by a near-endpoint expansion of Q. The rate, namely L and the fixed-scale exceedance p_tau, does not survive. There exist admissible shared class constants and two members of a smaller regularity class whose observed laws coincide exactly. Across the pair alpha agrees, whereas L and p_tau move. A degenerate Le Cam two-point bound excludes any uniformly consistent estimator of either, and pointwise consistency fails at one member. Only the rate needs an anchor. We conjecture that a known kernel family with known edge map identifies the rate fiber by fiber if and only if the family satisfies a fixed-scale injectivity clause, and we prove the sufficiency direction. In surrogate safety, uncalibrated conflict data give the shape of near-crash risk, not its absolute rate.
发表机构
- University of Washington（华盛顿大学）
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