Conformal geometry of statistical manifold with application to sequential estimation
Conformal geometry of statistical manifold with application to sequential estimation
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统计流形的共形几何及其在顺序估计中的应用
DOI：
10.1080/07474946.2011.593923
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
A.
中科院分区：
文献类型：
--
作者：
Kumon;M.;Takemura;A.;Takeuchi;A.
我们提出了一种分析序贯估计过程的几何方法。它基于Okamoto等人提出的二阶有效序贯估计的设计原理。通过引入对偶共形曲率量，阐明了序贯估计的协方差最小化的条件。这些条件进一步阐述了多维曲指数族。然后，通过使用典型的统计模型，冯米塞斯-费舍尔，和双曲面模型的理论结果进行数值研究。
We present a geometrical method for analyzing sequential estimating procedures. It is based on the design principle of the second-order efficient sequential estimation provided in Okamoto et al. . By introducing a dual conformal curvature quantity, we clarify the conditions for the covariance minimization of sequential estimators. These conditions are further elaborated for the multidimensional curved exponential family. The theoretical results are then numerically examined by using typical statistical models, von Mises-Fisher, and hyperboloid models.