Lehmann–Scheffé theorem

The set of Lehmann- Scheffé (named after Erich Leo Lehmann (20 November 1917 - September 12, 2009 ) and Henry Scheffé (April 11, 1907 - July 5, 1977 ) ) is a set of mathematical statistics, fundamental to the part results from the estimation theory.

Formulation

Be a statistical model for.

Be a picture.

Let further a suffiency and complete statistics.

Be an unbiased estimator for.

It exists with a measurable map.

Then uniformly most powerful unbiased estimator (at presence of the quadratic loss function ).

Interpretation

The set of Lehmann- Scheffé helps one to find a uniformly best unbiased estimators in the presence of suffizienten and complete statistics. Just as the set of Rao -Blackwell it provides criteria for best estimator.