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Unformatted text preview: PSTAT 120B  Probability & Statistics Class # 072 Efficiency, consistency, sufficiency review Jarad Niemi University of California, Santa Barbara 12 May 2010 Jarad Niemi (UCSB) Efficiency, consistency, sufficiency review 12 May 2010 1 / 16 Class overview Announcements Announcements Homework Homework 5 is returned No need for , proofs Show your work State theorems that you use, e.g. Factorization Theorem Midterm II Friday!! Covers 8.58.8,9.19.5 Show your work State theorems that you use, e.g. Factorization Theorem Jarad Niemi (UCSB) Efficiency, consistency, sufficiency review 12 May 2010 2 / 16 Class overview Goals Review of estimator properties Efficiency, consistency, sufficiency Example questions Jarad Niemi (UCSB) Efficiency, consistency, sufficiency review 12 May 2010 3 / 16 Efficiency review Definition Given two unbiased estimators 1 and 2 of a parameter , with variances V ( 1 ) and V ( 2 ), respectively, then the efficiency of 1 relative to 2 , denoted eff ( 1 , 2 ), is defined to be the ratio eff ( 1 , 2 ) = V ( 2 ) V ( 1 ) . Definition If is an unbiased estimator of , then under very general conditions V ( ) I ( ) = nE 2 log f ( Y ) 2 1 This is known as the Cram erRao lower bound . If an estimator has V ( ) = I ( ), the estimator is said to be efficient . E 2 log f ( Y ) 2 is often referred to as the Fisher information . Jarad Niemi (UCSB) Efficiency, consistency, sufficiency review 12 May 2010 4 / 16 Efficiency review Definition If is an unbiased estimator of , then the efficiency of , denoted eff ( ) is eff ( ) = I ( ) V ( ) ....
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This note was uploaded on 11/23/2010 for the course MATH 104b taught by Professor Ceniceros,h during the Spring '08 term at UCSB.
 Spring '08
 Ceniceros,H
 Statistics, Numerical Analysis, Probability

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