admissibility theorem
E766786
The admissibility theorem is a result in statistical decision theory that characterizes when a decision rule cannot be uniformly improved upon, linking admissible rules to optimality concepts such as those in complete class theorems.
All labels observed (1)
| Label | Occurrences |
|---|---|
| admissibility theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T8926741 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: admissibility theorem Context triple: [complete class theorem in decision theory, isRelatedTo, admissibility theorem]
-
A.
Szekeres–Lindström theorem
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
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B.
Halász theorem
Halász theorem is a fundamental result in analytic number theory that provides sharp bounds on the mean values of multiplicative functions, playing a key role in understanding their average behavior.
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C.
Subspace theorem
The Subspace theorem is a fundamental result in Diophantine approximation that describes how solutions to certain inequalities involving linear forms over algebraic numbers must lie in a finite union of proper subspaces.
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D.
Page theorem
The Page theorem is a result in quantum information theory and black hole physics that predicts how the entanglement entropy of a subsystem typically evolves, underpinning the characteristic "Page curve" behavior in discussions of the black hole information paradox.
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E.
Fitting lemma
The Fitting lemma is a result in group theory and module theory that characterizes how certain algebraic structures decompose into direct sums of invariant subcomponents, often involving nilpotent and invertible parts.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: admissibility theorem Target entity description: The admissibility theorem is a result in statistical decision theory that characterizes when a decision rule cannot be uniformly improved upon, linking admissible rules to optimality concepts such as those in complete class theorems.
-
A.
Szekeres–Lindström theorem
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
-
B.
Halász theorem
Halász theorem is a fundamental result in analytic number theory that provides sharp bounds on the mean values of multiplicative functions, playing a key role in understanding their average behavior.
-
C.
Subspace theorem
The Subspace theorem is a fundamental result in Diophantine approximation that describes how solutions to certain inequalities involving linear forms over algebraic numbers must lie in a finite union of proper subspaces.
-
D.
Page theorem
The Page theorem is a result in quantum information theory and black hole physics that predicts how the entanglement entropy of a subsystem typically evolves, underpinning the characteristic "Page curve" behavior in discussions of the black hole information paradox.
-
E.
Fitting lemma
The Fitting lemma is a result in group theory and module theory that characterizes how certain algebraic structures decompose into direct sums of invariant subcomponents, often involving nilpotent and invertible parts.
- F. None of above. chosen
Statements (35)
| Predicate | Object |
|---|---|
| instanceOf |
result in statistical decision theory
ⓘ
theorem ⓘ |
| appliesTo |
decision-theoretic formulations of statistical procedures
ⓘ
estimation problems ⓘ hypothesis testing problems ⓘ parametric statistical models ⓘ |
| assumes |
specified action space
ⓘ
specified loss function ⓘ specified parameter space ⓘ |
| characterizes |
conditions for admissibility of a decision rule
ⓘ
when a decision rule cannot be uniformly improved upon ⓘ |
| concerns | admissible decision rules ⓘ |
| contrastsWith | inadmissibility results ⓘ |
| field | statistical decision theory ⓘ |
| formalizes | notion of non-improvability of a decision rule ⓘ |
| framework |
Bayesian decision theory
ⓘ
frequentist decision theory ⓘ |
| goal | identify decision rules that cannot be uniformly improved in risk ⓘ |
| implies |
every admissible rule is in some complete class
ⓘ
under regularity conditions, Bayes rules are admissible ⓘ |
| links |
Bayes rules and admissible rules
ⓘ
admissible rules to optimality concepts ⓘ |
| relatedTo |
complete class theorem
ⓘ
linked to:
complete class theorem in decision theory
|
| relatesTo |
decision rules
ⓘ
loss functions ⓘ risk functions ⓘ |
| usedIn |
construction of optimal statistical procedures
ⓘ
evaluation of estimators ⓘ evaluation of tests ⓘ theoretical statistics ⓘ |
| usesConcept |
Bayes risk
ⓘ
complete class ⓘ prior distribution ⓘ risk dominance ⓘ uniform dominance ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: admissibility theorem Description of subject: The admissibility theorem is a result in statistical decision theory that characterizes when a decision rule cannot be uniformly improved upon, linking admissible rules to optimality concepts such as those in complete class theorems.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.