On Inequalities of Cramér-Rao Type and Admissibility Proofs

Blyth, Colin R.; Roberts, Donald M.

doi:10.1525/9780520325883-003

Cited by 7 publications

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“…An interesting problem concerns the choice of a measure of efficiency for the MLE in discrete parameter models: in his seminal paper, Hammersley [33] derives a generalization of Cramér-Rao inequality for the variance that is also valid when the parameter space is countable. The same inequality has been derived, in slightly more generality, in [12,16]. However, this choice is well-suited only in cases in which the MSE is a good measure of risk, for example, if the limiting distribution of the normalized estimator is normal.…”

Section: Optimality and Efficiencymentioning

confidence: 99%

Estimation in Discrete Parameter Models

Choirat¹,

Seri²

2012

Statist. Sci.

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In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points. In this case, we speak of discrete parameter models. Even though the problem is quite old and has interesting connections with testing and model selection, asymptotic theory for these models has hardly ever been studied. Therefore, we discuss consistency, asymptotic distribution theory, information inequalities and their relations with efficiency and superefficiency for a general class of m-estimators

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Section: Optimality and Efficiencymentioning

confidence: 99%