Rao Blackwell Theorem
The Rao-Blackwell Theorem is a fundamental result in statistics that provides a method for improving estimators. It states that if you have an unbiased estimator of a parameter, you can often find a better (or more efficient) estimator by conditioning on a sufficient statistic. This means that by using additional information from the data, you can reduce the variance of your estimator without introducing bias.
In practical terms, the theorem helps statisticians identify the best possible estimator for a given problem. By applying the Rao-Blackwell process, one can derive a new estimator that has desirable properties, making it more reliable for inference about the parameter of interest.