Conformal geometry of sequential test in multidimensional curved exponential family. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Kumon, Masayuki; Takemura, Akimichi; Takeuchi, Kei
• Is Part Of: Sequential analysis. Volume 35:Issue 1(2016)
• Page Start: 30
• Page End: 68
• Publication Date: 2016-01-02
• Subjects: Curved exponential family -- dual affine connections -- Euler-Schouten curvature -- hyperboloid distribution -- information geometry -- Riemannian metric -- Riemann-Christoffel curvature -- totally umbilic manifold -- von Mises-Fisher distribution; 62L12; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2016.1131570
• Languages: English
• ISSNs: 0747-4946

Abstract

ABSTRACT: 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.