Rao–Blackwell theorem  From Wikipedia, the free encyclopedia
Jump to: navigation, search  In statistics, the Rao–Blackwell
theorem, sometimes referred to as the Rao–Blackwell–Kolmogorov
theorem, is a result which characterizes the transformation of
an arbitrarily crude estimator into an estimator that is optimal
by the mean-squared-error criterion or any of a variety of
similar criteria.  The Rao–Blackwell theorem states that if g(X)
is any kind of estimator of a parameter θ, then the conditional
expectation of g(X) given T(X), where T is a sufficient
statistic, is typically a better estimator of θ, and is never
worse. Sometimes one can very easily construct a very crude
estimator g(X), and then evaluate that conditional expected
value to get an estimator that is in various senses optimal.
The theorem is named after Calyampudi Radhakrishna Rao and David
Blackwell. The process of transforming an estimator using the
Rao–Blackwell theorem is sometimes called Rao–Blackwellization.
The transformed estimator is ca