Rao-Blackwell Theorem
The Rao-Blackwell Theorem is a fundamental result in statistics that provides a method for improving an estimator. It states that if you have an unbiased estimator of a parameter, you can create a new estimator that is at least as good, and often better, by conditioning on a sufficient statistic. This new estimator will also be unbiased and have a lower variance.
In practical terms, the theorem helps statisticians find more efficient estimators by using additional information from the data. By focusing on sufficient statistics, which summarize the data without losing relevant information, the Rao-Blackwell Theorem ensures that the new estimator retains the desirable properties of the original while enhancing its performance.