class06-1-handouts

class06-1-handouts - PSTAT 120B - Probability &...

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Unformatted text preview: PSTAT 120B - Probability & Statistics Class # 06-1- Efficiency Jarad Niemi University of California, Santa Barbara 3 May 2010 Jarad Niemi (UCSB) Efficiency 3 May 2010 1 / 14 Class overview Announcements Announcements Homework Homework 4 due today by 4pm in SH 5521 Do not turn homework into my mailbox - you will now get a zero Mid-term II Friday 14 May Personal matter Jarad Niemi (UCSB) Efficiency 3 May 2010 2 / 14 Class overview Last time Intuition -2-1 1 2 2 4 6 8 10 mn 1:n.cis Jarad Niemi (UCSB) Efficiency 3 May 2010 3 / 14 Class overview Last time Consider Y 1 ,..., Y n iid N ( , 2 ). If 2 is known then y z / 2 / n is a 100(1- )% confidence interval for . If 2 is unknown then y t n- 1 ,/ 2 s / n is a 100(1- )% confidence interval for . Which interval is larger? It turns out E [ S ] = c 4 where c 4 = r 2 n- 1 ( n / 2) ([ n- 1] / 2) 1- 1 4 n- 7 32 n 2 . E t n- 1 ,/ 2 S / n z / 2 / n = t n- 1 ,/ 2 z / 2 E [ S ] = t n- 1 ,/ 2 z / 2 c 4 = t n- 1 ,/ 2 z / 2 c 4 Jarad Niemi (UCSB) Efficiency 3 May 2010 4 / 14 Class overview Goals Efficiency of estimators Cram er-Rao lower bound, exercise 9.8 Jarad Niemi (UCSB) Efficiency 3 May 2010 5 / 14 Efficiency Definition Given two unbiased estimators...
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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.

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class06-1-handouts - PSTAT 120B - Probability &...

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