Barankin bound
E621102
The Barankin bound is a fundamental lower bound in statistical estimation theory that generalizes and can be tighter than the Cramér–Rao bound for the variance of unbiased estimators, especially in non-regular or finite-sample settings.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Barankin bound canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6833723 — 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: Barankin bound Context triple: [Cramér–Rao bound, relatedConcept, Barankin bound]
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A.
Bounds
Bounds is the maiden surname of Lillian Disney, the wife of Walt Disney and a key figure in the early Disney family history.
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B.
Bounding Theory
Bounding Theory is a subtheory within Government and Binding Theory in generative linguistics that constrains how far syntactic elements can move in a sentence.
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C.
Berry–Esseen theorem
The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
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D.
Grothendieck inequality
The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
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E.
Banach limit
A Banach limit is a linear functional on the space of bounded sequences that extends the usual limit and assigns generalized “limits” to sequences that may not converge in the classical sense.
- 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: Barankin bound Target entity description: The Barankin bound is a fundamental lower bound in statistical estimation theory that generalizes and can be tighter than the Cramér–Rao bound for the variance of unbiased estimators, especially in non-regular or finite-sample settings.
-
A.
Bounds
Bounds is the maiden surname of Lillian Disney, the wife of Walt Disney and a key figure in the early Disney family history.
-
B.
Bounding Theory
Bounding Theory is a subtheory within Government and Binding Theory in generative linguistics that constrains how far syntactic elements can move in a sentence.
-
C.
Berry–Esseen theorem
The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
-
D.
Grothendieck inequality
The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
-
E.
Banach limit
A Banach limit is a linear functional on the space of bounded sequences that extends the usual limit and assigns generalized “limits” to sequences that may not converge in the classical sense.
- F. None of above. chosen
Statements (41)
| Predicate | Object |
|---|---|
| instanceOf |
lower bound in estimation theory
ⓘ
statistical bound ⓘ |
| appliesTo | unbiased estimators ⓘ |
| canBe | tighter than Cramér–Rao bound ⓘ |
| canHandle |
bounded parameter spaces
ⓘ
discrete parameter spaces ⓘ non-differentiable likelihood functions ⓘ |
| characterizes | minimum achievable variance of unbiased estimators ⓘ |
| comparedTo |
Bhattacharyya bound
ⓘ
linked to:
Bhattacharyya distance
Cramér–Rao bound ⓘ Hammersley–Chapman–Robbins bound ⓘ |
| dependsOn |
family of probability distributions
ⓘ
parameter point of interest ⓘ set of alternative parameter values ⓘ |
| doesNotRequire | regularity conditions of Cramér–Rao bound ⓘ |
| field |
mathematical statistics
ⓘ
statistical estimation theory ⓘ |
| generalizes | Cramér–Rao bound ⓘ |
| goal | characterize fundamental limits of estimation accuracy ⓘ |
| hasFormulation | optimization over finite sets of parameter points ⓘ |
| hasProperty |
can be approximated numerically
ⓘ
can be difficult to compute exactly ⓘ |
| introducedIn | 20th century ⓘ |
| namedAfter | Eugene Barankin ⓘ |
| provides |
lower bound on covariance matrix of unbiased estimators
ⓘ
performance benchmark for estimators ⓘ |
| relatedTo |
Fisher information
ⓘ
information inequality ⓘ minimum variance unbiased estimation ⓘ |
| typeOf | local lower bound ⓘ |
| usedAs |
benchmark for estimator design
ⓘ
tool for performance analysis in engineering systems ⓘ |
| usedIn |
array processing
ⓘ
communications theory ⓘ direction-of-arrival estimation ⓘ finite-sample settings ⓘ non-regular estimation problems ⓘ parametric estimation ⓘ signal processing ⓘ |
| validFor |
finite samples
ⓘ
non-asymptotic analysis ⓘ |
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: Barankin bound Description of subject: The Barankin bound is a fundamental lower bound in statistical estimation theory that generalizes and can be tighter than the Cramér–Rao bound for the variance of unbiased estimators, especially in non-regular or finite-sample settings.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.