Barankin bound

E621102

lower bound in estimation theory statistical bound

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.

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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 NERFINISHED ⓘ Cramér–Rao bound NERFINISHED ⓘ Hammersley–Chapman–Robbins bound NERFINISHED ⓘ
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 NERFINISHED ⓘ
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 NERFINISHED ⓘ
provides	lower bound on covariance matrix of unbiased estimators ⓘ performance benchmark for estimators ⓘ
relatedTo	Fisher information NERFINISHED ⓘ 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 ⓘ

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

Cramér–Rao bound → relatedConcept → Barankin bound ⓘ