Warped Metrics for Location-Scale Models View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2017-10-24

AUTHORS

Salem Said , Yannick Berthoumieu

ABSTRACT

This paper argues that a class of Riemannian metrics, called warped metrics, plays a fundamental role in statistical problems involving location-scale models. The paper reports three new results: (i) the Rao-Fisher metric of any location-scale model is a warped metric, provided that this model satisfies a natural invariance condition, (ii) the analytic expression of the sectional curvature of this metric, (iii) the exact analytic solution of the geodesic equation of this metric. The paper applies these new results to several examples of interest, where it shows that warped metrics turn location-scale models into complete Riemannian manifolds of negative sectional curvature. This is a very suitable situation for developing algorithms which solve problems of classification and on-line estimation. Thus, by revealing the connection between warped metrics and location-scale models, the present paper paves the way to the introduction of new efficient statistical algorithms. More... »

PAGES

631-638

References to SciGraph publications

Book

TITLE

Geometric Science of Information

ISBN

978-3-319-68444-4
978-3-319-68445-1

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-68445-1_73

DOI

http://dx.doi.org/10.1007/978-3-319-68445-1_73

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1092381058


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