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Theorem

Rao-Blackwell Theorem

Probability and Statistics

Given any unbiased estimator of a parameter, conditioning it on a sufficient statistic produces a new unbiased estimator whose variance is no larger, and generally smaller. Named for C. R. Rao and David Blackwell, it is a foundational result of statistical estimation theory.

Facts
Statement
In statistics, the Rao-Blackwell theorem, sometimes referred to as the Rao-Blackwell-Kolmogorov theorem, is a result that 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. 1
Classification
Statement Form
Characterization Theorem 1
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Proved By

Source Rao-Blackwell Theorem (Wikipedia)
Sources
1. Rao-Blackwell Theorem (Wikipedia)
Wikimedia Foundation
  • Lead section, first sentence
    In statistics, the Rao-Blackwell theorem, sometimes referred to as the Rao-Blackwell-Kolmogorov theorem, is a result that 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.
  • Proved By: David Blackwell, Lead paragraph
    In statistics, the Rao-Blackwell theorem, sometimes referred to as the Rao-Blackwell-Kolmogorov theorem, is a result that characterizes the transformation
  • In Group: Mathematical Statistics and Estimation, Lead section
    In statistics, the Rao-Blackwell theorem, sometimes referred
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