David Blackwell

Kiarra Terry

Biography

David Blackwell is, to mathematicians, the most famous, perhaps greatest, African American Mathematician. He earned his Bachelor of Arts in Mathematics in 1938, Master of Arts in Mathematics in 1939, and his Ph.D. in 1941 (at the age of 22), all from the University of Illinois. He is the seventh African American to receive a Ph.D. in Mathematics. He is the first and only African American to be any one of: a member of the National Academy of Sciences, a President of the American Statistical Society, and a Vice President of the America Mathematics Society.

Blackwell theorem

This was also known as the Rao-Blackwell Theorem which consisted of dynamic programming, game theory, measuring theory, probability theory, set theory, and mathematical statistics. These theories are very famous and are still being used today.

More Information

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 suff., 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 called the Rao–Blackwell estimator.