Complete statistic
Definition taught in Exponential families and conjugacy, part of Bayesian statistics
Complete statistic
| Type | Definition |
| Taught in | Exponential families and conjugacy |
| Part | Bayesian statistics |
| Properties | 1 |
| Questions using it | 2 |
A statistic T is complete for a family if
\mathbb{E}_\theta\{q(T)\}=0,\qquad \theta\in\Omega,
implies q(T)=0 almost surely for every \theta\in\Omega.
Properties
Basu’s theorem
Main article: Basu’s theorem
A complete sufficient statistic is independent of every ancillary statistic.
Used in
- Taught in Exponential families and conjugacy, where the derivation and examples are.
- Questions that use it (2) — Q24 (answer) · Question 5 (answer)
- All 18 questions on Exponential families and conjugacy
See also
Statistic and estimator · Sufficient statistic · Fisher–Neyman factorisation · Minimal sufficiency · Ancillary statistic · Basu’s theorem · Natural exponential family · Translation to another common notation