Pitman–Koopman–Darmois, informal form
Theorem taught in Exponential families and conjugacy, part of Bayesian statistics
Pitman–Koopman–Darmois, informal form
| Type | Theorem |
| Taught in | Exponential families and conjugacy |
| Part | Bayesian statistics |
For regular iid models with parameter-independent support, the theorem says, roughly, that the existence for every n of a sufficient statistic whose dimension stays fixed essentially characterises exponential families. The support condition matters: models such as \operatorname{Uniform}(0,\theta) can have a fixed-dimensional sufficient statistic without having the regular form Equation (3) in Exponential families and conjugacy.
Used in
- Taught in Exponential families and conjugacy, where the derivation and examples are.
- All 18 questions on Exponential families and conjugacy
See also
Sufficient statistic · Exponential family · Statistic and estimator · Fisher–Neyman factorisation · Minimal sufficiency · Complete statistic · Ancillary statistic · Basu’s theorem