Rao-blackwell Theorem

SOME PREREQUISITE DEFINITIONS

An Estimator δ(''X'') is an ''observable'' random variable (i.e. a Statistic ) used for estimating some ''unobservable'' quantity. For example, one may be unable to observe the average height of ''all'' male students at the University of X, but one may observe the heights of a random sample of 40 of them. The average height of those 40--the "sample average"--may be used as an estimator of the unobservable "population average".

A Sufficient Statistic ''T''(''X'') is an ''observable'' Random Variable such that the Conditional Probability distribution of all observable data ''X'' given ''T''(''X'') does not depend on any of the ''unobservable'' quantities such as the mean or standard deviation of the whole population from which the data ''X'' was taken. In the most frequently cited examples, the "unobservable" quantities are parameters that parametrize a known family of Probability Distribution s according to which the data are distributed.

:<math>\delta 1

E(\delta_0X_1+\cdots+X_n)</math>

Information About