Barbaresco
Frédéric
Statistics
en
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.
true
2017-10-24
chapters
chapter
631-638
2019-04-16T05:01
2017-10-24
https://link.springer.com/10.1007%2F978-3-319-68445-1_73
https://scigraph.springernature.com/explorer/license/
Warped Metrics for Location-Scale Models
978-3-319-68444-4
978-3-319-68445-1
Geometric Science of Information
Berthoumieu
Yannick
10.1007/978-3-319-68445-1_73
doi
Laboratoire IMS (CNRS - UMR 5218), Université de Bordeaux, Bordeaux, France
University of Bordeaux
Mathematical Sciences
Salem
Said
Frank
Nielsen
Springer International Publishing
Cham
pub.1092381058
dimensions_id
readcube_id
9db0074d7c1742438d83e3834a0054a4c5bb3232f11c95b19d168c87299c2d12
Springer Nature - SN SciGraph project