Gw mau tau Teorema dari Téoréma Rao-Blackwell. Jelasin dalam bahasa sunda

Salah sahiji téorema Rao-Blackwell nyebutkeun:

Kuadrat kasalahan mean ti estimator Rao-Blackwell teu leuwih gedé tina estimator asli.

Téori nu leuwih ilahar dipaké saperti kieu.

Hal nu leuwih penting keur dibuktikeun tinimbang hal di luhur nyaéta law of total expectation sarta kanyaatan keur sakabéh variabel  Y, E(Y2) teu bisa kurang ti [E(Y)]2.  That inequality is a case of Jensen's inequality, although in a statistics course it may be shown to follow instantly from the frequently mentioned fact that

The more general version of the Rao-Blackwell théorem spéaks of the "expected loss"

where the "loss function" L may be any convex function.  For the proof of the more general version, Jensen's inequality cannot be dispensed with.

The improved éstimator is unbiased if and only if the original éstimator is unbiased, as may be seen at once by using the law of total expectation.  The théorem holds regardless of whether biased or unbiased éstimators are used.

The théorem seems very wéak: it says only that the allegedly improved éstimator is no worse than the original éstimator.  In practice, however, the improvement is often enormous, as an example can show.