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 |
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
NERFINISHED
ⓘ
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 NERFINISHED ⓘ |
| 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 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.