Conformal geometry of sequential test in multidimensional curved exponential family
Conformal geometry of sequential test in multidimensional curved exponential family
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多维曲线指数族序贯检验的共形几何
DOI：
10.1080/07474946.2016.1131570
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
A.Takemura and Kei Takeuchi
中科院分区：
文献类型：
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作者：
Masayuki Kumon;A.Takemura and Kei Takeuchi
本文提出了一种分析序贯测试过程的微分几何方法。它基于Kumon等人（2011）发展的统计流形的共形几何的初步结果。通过引入曲率型随机变量，首先阐明了在适当的序贯检验程序下统计流形为指数族的条件。这一结果为研究多维曲线指数族的有效序贯检验提供了进一步的理论依据。用von Mises-Fisher和双曲面模型对理论结果进行了数值检验。
This article presents a differential geometrical method for analyzing sequential test procedures. It is based on the primal result on the conformal geometry of statistical manifold developed in Kumon et al. (2011). By introducing curvature-type random variables, the condition is first clarified for a statistical manifold to be an exponential family under an appropriate sequential test procedure. This result is further elaborated for investigating the efficient sequential test in a multidimensional curved exponential family. The theoretical results are numerically examined by using von Mises-Fisher and hyperboloid models.