Amari–Chentsov structure on the statistical manifold of models for accelerated life tests

Amari–Chentsov structure on the statistical manifold of models for accelerated life tests TEST https://doi.org/10.1007/s11749-018-0587-1 ORIGINAL PAPER Amari–Chentsov structure on the statistical manifold of models for accelerated life tests 1,3 2 Fode Zhang · Hon Keung Tony Ng · 3 3 Yimin Shi · Ruibing Wang Received: 7 May 2017 / Accepted: 16 May 2018 © Sociedad de Estadística e Investigación Operativa 2018 Abstract The invariant geometric structures on the statistical manifold under suf- ficient statistics have played an important role in both statistical inference and information theory. In this paper, we focus on one of the commonly used invari- ant geometric structures, the Amari–Chentsov structure, on a statistical manifold. The manifold is derived from statistical models for accelerated life tests (ALTs) with cen- soring based on the exponential family of distributions. The constant-stress ALTs and step-stress ALTs are considered. We show that the statistical manifold still belongs to the exponential family of distributions, but the cumulant generating function depends on a random variable related to the experimental design of the ALT, which is different from the usual situation. We also investigate the Bregman divergence and Riemannian metric. The relationships between the Riemannian metric and the expected Fisher information metric are studied. The dual coordinate system is studied by using the Legendre http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png TEST Springer Journals

Amari–Chentsov structure on the statistical manifold of models for accelerated life tests

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Sociedad de Estadística e Investigación Operativa
Subject
Statistics; Statistics, general; Statistical Theory and Methods; Statistics for Business/Economics/Mathematical Finance/Insurance
ISSN
1133-0686
eISSN
1863-8260
D.O.I.
10.1007/s11749-018-0587-1
Publisher site
See Article on Publisher Site

Abstract

TEST https://doi.org/10.1007/s11749-018-0587-1 ORIGINAL PAPER Amari–Chentsov structure on the statistical manifold of models for accelerated life tests 1,3 2 Fode Zhang · Hon Keung Tony Ng · 3 3 Yimin Shi · Ruibing Wang Received: 7 May 2017 / Accepted: 16 May 2018 © Sociedad de Estadística e Investigación Operativa 2018 Abstract The invariant geometric structures on the statistical manifold under suf- ficient statistics have played an important role in both statistical inference and information theory. In this paper, we focus on one of the commonly used invari- ant geometric structures, the Amari–Chentsov structure, on a statistical manifold. The manifold is derived from statistical models for accelerated life tests (ALTs) with cen- soring based on the exponential family of distributions. The constant-stress ALTs and step-stress ALTs are considered. We show that the statistical manifold still belongs to the exponential family of distributions, but the cumulant generating function depends on a random variable related to the experimental design of the ALT, which is different from the usual situation. We also investigate the Bregman divergence and Riemannian metric. The relationships between the Riemannian metric and the expected Fisher information metric are studied. The dual coordinate system is studied by using the Legendre

Journal

TESTSpringer Journals

Published: May 30, 2018

References

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