Statistic and estimator
Definition taught in Exponential families and conjugacy, part of Bayesian statistics
Statistic and estimator
| Type | Definition |
| Taught in | Exponential families and conjugacy |
| Part | Bayesian statistics |
Write the complete sample as {\boldsymbol{X}}=(X_1,\ldots,X_n) and its realised value as {\boldsymbol{x}}=(x_1,\ldots,x_n). A statistic is any function
T=T({\boldsymbol{X}})
of the random data alone. It cannot contain an unknown parameter. An estimator is a statistic used to estimate a parameter or a function of one, so every estimator is a statistic but not every statistic is introduced for estimation. For example, \overline X, \max_iX_i, and \sum_i(X_i-\overline X)^2 are all statistics.
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 · Fisher–Neyman factorisation · Minimal sufficiency · Complete statistic · Ancillary statistic · Basu’s theorem · Natural exponential family · Translation to another common notation