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Keywords = Blackwell sufficiency

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11 pages, 298 KiB  
Article
Generalizations of Rao–Blackwell and Lehmann–Scheffé Theorems with Applications
by Seyf Alemam, Hazhir Homei and Saralees Nadarajah
Mathematics 2023, 11(19), 4146; https://doi.org/10.3390/math11194146 - 30 Sep 2023
Cited by 1 | Viewed by 2704
Abstract
Our aim in this paper is extending the applicability domain of the Rao–Blackwell theorem, our methodology is using conditional expectation and generalizing sufficient statistics, and one result is a generalization of the Lehmann–Scheffé theorem; as a conclusion, some problems that could not be [...] Read more.
Our aim in this paper is extending the applicability domain of the Rao–Blackwell theorem, our methodology is using conditional expectation and generalizing sufficient statistics, and one result is a generalization of the Lehmann–Scheffé theorem; as a conclusion, some problems that could not be solved by an earlier version of the Lehmann–Scheffé theorem become solvable by our new generalization. Full article
11 pages, 203 KiB  
Article
Statistical Information: A Bayesian Perspective
by Rafael B. Stern and Carlos A. de B. Pereira
Entropy 2012, 14(11), 2254-2264; https://doi.org/10.3390/e14112254 - 7 Nov 2012
Cited by 2 | Viewed by 6242
Abstract
We explore the meaning of information about quantities of interest. Our approach is divided in two scenarios: the analysis of observations and the planning of an experiment. First, we review the Sufficiency, Conditionality and Likelihood principles and how they relate to trivial experiments. [...] Read more.
We explore the meaning of information about quantities of interest. Our approach is divided in two scenarios: the analysis of observations and the planning of an experiment. First, we review the Sufficiency, Conditionality and Likelihood principles and how they relate to trivial experiments. Next, we review Blackwell Sufficiency and show that sampling without replacement is Blackwell Sufficient for sampling with replacement. Finally, we unify the two scenarios presenting an extension of the relationship between Blackwell Equivalence and the Likelihood Principle. Full article
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