sufficient statistics

(1 hours to learn)


Sufficient statistics are statistics which summarize all of the information a dataset contains about the parameters of a distribution. The Rao-Blackwell Theorem implies that statistical estimators should depend only on sufficient statistics when they exist.


This concept has the prerequisites:


  • Know the definition of a sufficient statistic
  • Derive an equivalent criterion in terms of a factorization of the distribution
  • Prove the Rao-Blackwell Theorem, which implies that estimators should be based on sufficient statistics when the exist.
    • Note: the general form of the Rao-Blackwell Theorem, which applies to convex loss functions, depends on Jensen's inequality , but many texts give the special case for squared error.

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