The Cramér-Rao inequality on singular statistical models I

We introduce the notion of the essential tangent bundle of a parametrized measure model and the notion of reduced Fisher metric on a (possibly singular) 2-integrable measure model. Using these notions and a new characterization of \(k\)-integrable parametrized measure models, we extend the Cramér-Ra...

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Bibliographic Details
Published in:arXiv.org 2017-07
Main Authors: Jost, Jürgen, Lê, Hông Vân, Lorenz Schwachhöfer
Format: Article
Language:English
Subjects:
Inequality
Parameterization
Statistical models
Online Access:Get full text
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Summary:We introduce the notion of the essential tangent bundle of a parametrized measure model and the notion of reduced Fisher metric on a (possibly singular) 2-integrable measure model. Using these notions and a new characterization of \(k\)-integrable parametrized measure models, we extend the Cramér-Rao inequality to \(2\)-integrable (possibly singular) statistical models for general \(\varphi\)-estimations, where \(\varphi\) is a \(V\)-valued feature function and \(V\) is a topological vector space. Thus we derive an intrinsic Cramér-Rao inequality in the most general terms of parametric statistics.
ISSN:2331-8422