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National Repository of Grey Literature 1 records found  Search took 0.00 seconds. 
The Cramér-Rao inequality on singular statistical models
 Le, Hong-Van ; Jost, J. ; Schwachhöfer, L.
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.
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