Original title: The Cramér-Rao inequality on singular statistical models
Authors: Le, Hong-Van ; Jost, J. ; Schwachhöfer, L.
Document type: Papers
Conference/Event: Third International Conference, Geometric Science of Information, GSI 2017, Paris (FR), 20171107
Year: 2017
Language: eng
Abstract: We introduce the notions of essential tangent space and reduced Fisher metric and extend the classical Cramér-Rao inequality to $2$-integrable (possibly singular) statistical models for general $varphi$-estimators, where $varphi$ is a $V$-valued feature function and $V$ is a topological vector space. We show the existence of a $varphi$-efficient estimator on strictly singular statistical models associated with a finite sample space and on a class of infinite dimensional exponential models that have been discovered by Fukumizu. We conclude that our general Cramér-Rao inequality is optimal.
Keywords: Cramér-Rao inequality; Singular Statistical Models
Host item entry: Geometric Science of Information. GSI 2017, ISBN 978-3-319-68444-4, ISSN 0302-9743
Note: Související webová stránka: https://link.springer.com/chapter/10.1007%2F978-3-319-68445-1_64

Institution: Institute of Mathematics AS ČR (web)
Document availability information: Fulltext is available on demand via the digital repository of the Academy of Sciences.
Original record: http://hdl.handle.net/11104/0276907

Permalink: http://www.nusl.cz/ntk/nusl-373307


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