混合离散-连续计数数据的广义Fiducial推断：理论与应用
Generalized Fiducial Inference for Hybrid Discrete-Continuous Count Data: Theory and Application
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中文总结 AI 辅助
针对高频运动员追踪计数数据，提出混合广义Fiducial框架，结合精确负二项与正态近似，实现无先验的不确定性量化，并证明理论性质，实证显示效应无法与噪声区分。
中文摘要 AI 辅助
高频运动员追踪数据可概括为分位数立方体（Thomas和Hannig，《体育定量分析杂志》，2026）：即速度、加速度和运动角度分箱中花费时间的计数。在我们的应用中，每个运动员-比赛会话有100个这样的分箱，计数从不到一百到几千不等。一个分箱的负二项分布是否接近正态取决于其形状参数，即均值与离散参数的乘积，而非仅取决于计数本身。我们开发了一个混合广义Fiducial框架，在估计形状较小时使用精确的负二项结构方程，在形状较大时使用矩匹配的正态近似，从而在没有先验的情况下为数百个回归和离散参数提供不确定性量化。只有正态分量对Fiducial Jacobian有贡献，该Jacobian为闭式块对角形式，并且我们证明了正确指定的混合模型的Bernstein-von Mises定理。模拟显示接近名义覆盖概率，与平坦先验贝叶斯分析一致，并且分区应基于估计的形状而非均值或观测响应。在来自17名职业女子足球运动员的216个会话中，估计的位置和年龄效应集中在速度极值和最高加速度处，但运动员级别的置换检验显示这些模式无法与标签噪声区分开来。
英文摘要
High-frequency athlete-tracking data can be summarized as quantile cubes (Thomas and Hannig, Journal of Quantitative Analysis in Sports, 2026): counts of time spent in bins of velocity, acceleration and movement angle. In our application each athlete-match session has 100 such bins, with counts from under a hundred to several thousand. Whether a bin's negative binomial distribution is close to normal depends on its shape, the product of mean and dispersion, not on the count alone. We develop a hybrid generalized fiducial framework that uses exact negative binomial structural equations where the estimated shape is small and moment-matched normal approximations where it is large, providing uncertainty quantification for hundreds of regression and dispersion parameters without a prior. Only the normal components contribute to the fiducial Jacobian, which is block diagonal in closed form, and we prove a Bernstein-von Mises theorem for the correctly specified hybrid model. Simulations show near-nominal coverage, agreement with a flat-prior Bayesian analysis, and that the partition should be based on the estimated shape rather than on the mean or the observed responses. In 216 sessions from 17 professional women's soccer athletes, the estimated position and age effects concentrate at the velocity extremes and highest accelerations, but an athlete-level permutation check shows these patterns cannot be distinguished from label noise.
发表机构
- Department of Statistics and Operations Research, University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校统计与运筹学系）
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