Rao–Blackwell theorem

The set of Rao -Blackwell is a set of mathematical statistics, which is one of the basic results from the theory of point estimation. Together with the set of Lehmann- Scheffé it provides criteria for best estimator.

It is named after the Indian mathematician CR Rao and his U.S. colleague David Blackwell.

Formulation

Be a statistical model for a picture and an estimator for. Let further a sufficient statistic.

Then is defined by an estimator. This estimator has the same bias as, and continues to apply:

This is referred to as the mean square deviation (English mean squared error ).

In the above inequality strict inequality is valid, if not already is a function of.

Interpretation

The set of Rao -Blackwell turns out that each estimator can be improved for a parameter in that it requires him to a sufficient statistic. Best estimates can be therefore necessarily represent as functions of such statistics.