The Lehmann-Scheffe Theorem states that if a statistic is complete and sufficient for a parameter and is also unbiased for some estimable function of that parameter, then it is the unique minimum-variance unbiased estimator of that function. Named for Erich Lehmann and Henry Scheffe, it gives the standard route in classical statistical theory for proving a proposed estimator is the best possible unbiased one, once completeness and sufficiency have already been established for the underlying statistic.
Facts
StatementAny unbiased estimator that depends on the data only through a complete, sufficient statistic is the unique uniformly minimum-variance unbiased estimator (UMVUE) of its expectation. 2 Classification
Statement Form Sources
1. Wikipedia: Lehmann-Scheffé theorem
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
The theorem states that any unbiased estimator for a quantity that depends on the data only through a complete, sufficient statistic is the unique uniformly minimum-variance unbiased estimator (UMVUE) of that quantity.
2. Lehmann-Scheffe theorem (Wikipedia)
Statement sectionQuote, Statement section
any unbiased estimator for a quantity that depends on the data only through a complete, sufficient statistic is the unique uniformly minimum-variance unbiased estimator (UMVUE) of that quantity.
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.