Yoshioka Masaki, Tanaka Fuyuhiko
Graduate School of Engineering Science, Osaka University, Osaka 560-8531, Japan.
Center for Education in Liberal Arts and Sciences, Osaka University, Osaka 560-0043, Japan.
Entropy (Basel). 2023 May 8;25(5):769. doi: 10.3390/e25050769.
In information geometry, there has been extensive research on the deep connections between differential geometric structures, such as the Fisher metric and the -connection, and the statistical theory for statistical models satisfying regularity conditions. However, the study of information geometry for non-regular statistical models is insufficient, and a one-sided truncated exponential family (oTEF) is one example of these models. In this paper, based on the asymptotic properties of maximum likelihood estimators, we provide a Riemannian metric for the oTEF. Furthermore, we demonstrate that the oTEF has an = 1 parallel prior distribution and that the scalar curvature of a certain submodel, including the Pareto family, is a negative constant.
在信息几何中，对于诸如费希尔度量和(\Gamma -)联络等微分几何结构与满足正则条件的统计模型的统计理论之间的深层联系，已经有了广泛的研究。然而，对非正则统计模型的信息几何研究并不充分，单边截断指数族（oTEF）就是这类模型的一个例子。在本文中，基于最大似然估计量的渐近性质，我们为oTEF提供了一种黎曼度量。此外，我们证明了oTEF具有一个(\alpha = 1)的平行先验分布，并且包括帕累托族在内的某个子模型的标量曲率是一个负常数。
