论文标题
非参数估计和差异渔民度量
Nonparametric estimations and the diffeological Fisher metric
论文作者
论文摘要
在本文中，首先，我们使用概率形态的功能性语言调查了差异性渔民度量标准及其自然性的概念，并在\ cite {le2020}中稍微扩展了Lê的理论，以包括弱$ c^k $ -Diffeological统计学模型。然后，我们介绍了差异渔民距离的产生概念，即差异学Hausdorff-Jeffrey测量，并解释了它们在统计中的古典和贝叶斯非参数估计问题中的作用。
In this paper, first, we survey the concept of diffeological Fisher metric and its naturality, using functorial language of probability morphisms, and slightly extending Lê's theory in \cite{Le2020} to include weakly $C^k$-diffeological statistical models. Then we introduce the resulting notions of the diffeological Fisher distance, the diffeological Hausdorff--Jeffrey measure and explain their role in classical and Bayesian nonparametric estimation problems in statistics.
