Lehmann–Scheffé theorem
Topic of Exponential families and conjugacy, part of Bayesian statistics
Lehmann–Scheffé theorem
| Type | Topic |
| Taught in | Exponential families and conjugacy |
| Part | Bayesian statistics |
An unbiased estimator that is a function of a complete sufficient statistic is the unique uniformly minimum-variance unbiased estimator of its expectation.
In Exponential families and conjugacy
Sufficiency concerns lossless data reduction; completeness concerns whether a nonzero function of the reduced data can have mean zero for every parameter value. A complete sufficient statistic is minimal sufficient. The Lehmann–Scheffé theorem further says that an unbiased estimator which is a function of a complete sufficient statistic is the unique uniformly minimum-variance unbiased estimator of its target. The variance inequality that reduces the search to functions of a sufficient statistic is the Rao–Blackwell theorem.
Used in
See also
Unbiased estimator · Sufficient statistic · Uniformly minimum-variance unbiased estimator · Estimator · Expectation · Statistic and estimator · Fisher–Neyman factorisation · Minimal sufficiency