论文标题
1D位置尺度模型中的Wasserstein统计数据
Wasserstein statistics in 1D location-scale model
论文作者
论文摘要
Wasserstein几何形状和信息几何形状是在概率分布的多种形式中引入的两个重要结构。前者是通过使用两个分布之间的运输成本来定义的，因此它反映了定义分布的基本歧管的度量结构。信息几何形状是基于不变性标准构建的，即在基本空间的可逆转换下几何形状是不变的。两者都有自己的应用程序。统计推断是在信息几何形状上构建的，其中Fisher指标起着基本作用，而Wasserstein几何形状对于应用于计算机视觉和AI的应用很有用。在基本空间是1维的情况下，我们提出了基于Wasserstein几何形状的统计推断。通过使用位置尺度模型，我们明确地得出了$ W $估计器并研究其渐近行为。
Wasserstein geometry and information geometry are two important structures introduced in a manifold of probability distributions. The former is defined by using the transportation cost between two distributions, so it reflects the metric structure of the base manifold on which distributions are defined. Information geometry is constructed based on the invariance criterion that the geometry is invariant under reversible transformations of the base space. Both have their own merits for applications. Statistical inference is constructed on information geometry, where the Fisher metric plays a fundamental role, whereas Wasserstein geometry is useful for applications to computer vision and AI. We propose statistical inference based on the Wasserstein geometry in the case that the base space is 1-dimensional. By using the location-scale model, we derive the $W$-estimator explicitly and studies its asymptotic behaviors.
