Lecture10_412

# Lecture10_412 - AMS412 Lecture 10 Cramer-Rao Lower Bound...

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1 AMS412 Lecture 10. Cramer-Rao Lower Bound, Efficient Estimator, Best Estimator Unbiased Estimator of , say It could be really difficult for us to compare when there are many of them. Theorem. Cramer-Rao Lower Bound Let be a random sample from a population with p.d.f. . Let be an unbiased estimator of . Given some regularity conditions (continuous differentiable etc.) and the domain of . does not depend on . Then, we have Theorem. Properties of the MLE Let Let be the MLE of , then The MLE is asymptotically unbiased and its asymptotic variance : C-R lower bound

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2 Harald Cramér (left) was born in Stockholm , Sweden on September 25, 1893, and died there on October 25, 1985 . (wiki). Calyampudi Radhakrishna Rao (right) , FRS known as C R Rao (born 10 September 1920) is an Indian statistician . He is professor emeritus at Penn State University and Research Professor at the University at Buffalo . Rao was awarded the US National Medal of Science in 2002. (wiki) Example 1. Let 1. MLE of p ?
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