多维曲线指数族中序贯检验的共形几何
Conformal Geometry of Sequential Test in Multidimensional Curved Exponential Family
摘要：
本文提出一种分析序贯检验程序的微分几何方法。它基于Kumon，Takemura and Takeuchi（2011）在统计流形的共形几何上的初步结果。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指数族的有效序贯检验提供了进一步的解释。用von Mises-Fisher和双曲面模型对理论结果进行了数值检验。
英文摘要：
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, Takemura and Takeuchi (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.
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