Mathematical Statistics (2024): Lecture 28

Sufficient Statistics and the Rao-Blackwell Theorem

In this video:
🔹Definition of a Sufficient Statistic 1:25
🔹The Factorization Criterion for Sufficiency 4:42
🔹Bernoulli Distribution Example 11:17
🔹Exponential Distribution Example 17:47
🔹Normal Distribution Example 20:56
🔹Uniform Distribution Example 28:35
🔹Beta Distribution Example 33:03
🔹Conditional Expectation and Variance 37:54
🔹The Rao-Blackwell Theorem 51:55

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[amorphous]

When T*=T, so T* has smallest variance...so is there any relation between Var(T*) and CRLB(like would they be equal) ... or is it something that will depend on T(the initial unbiased estimator we started with(like we would have gotten better T* with some other T i.e.., with smaller variance)?