论文标题
基准在作用中
Fiducial Symmetry in Action
论文作者
论文摘要
对称是古典和现代物理学的关键。一个显着的例子是由于Noether定理的时间变化而导致的能量保存。对称性同样是统计中的关键要素，该要素也是物理学为现实世界现象提供模型。充分性，条件性和不变性是基本原理的例子。 Galili和Meilijson（2016）和Mandel（2020）通过考虑缩放统一模型很好地说明了前两个原则。我们通过提供进一步的结果来说明第三个原理，从而通过对称考虑因素为缩放统一提供最佳的推断。通过依靠Fisher（1930）发起的基准论点来简化证明。 关键字：数据生成方程；最佳的模棱两可的估计；规模家庭；条件性原则；最小的足够；均匀分布；
Symmetry is key in classical and modern physics. A striking example is conservation of energy as a consequence of time-shift invariance from Noether's theorem. Symmetry is likewise a key element in statistics, which, as also physics, provide models for real world phenomena. Sufficiency, conditionality, and invariance are examples of basic principles. Galili and Meilijson (2016) and Mandel (2020) illustrate the first two principles very nicely by considering the scaled uniform model. We illustrate the third principle by providing further results which give optimal inference for the scaled uniform by symmetry considerations. The proofs are simplified by relying on fiducial arguments as initiated by Fisher (1930). Keywords: Data generating equation; Optimal equivariant estimate; Scale family; Conditionality principle; Minimal sufficient; Uniform distribution;
