Stat 5132 (Geyer) Old First Midterm

# Stat 5132 (Geyer) Old First Midterm - it. Problem 4 Suppose...

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Up: Stat 5132 Stat 5132 First Midterm Exam, February 4, 1998 Problem 1 Let be the sample median for an i. i. d. sample of size n from the model having densities where is an unknown parameter, .Find the asymptotic distribution of . Problem 2 Let X 1 , X 2 , , X n be an i. i. d. sample from a model, and let S 2 n be the sample variance Calculate the probability in the case n = 10. Problem 3 Let X 1 , X 2 , , X n be an i. i. d. sample from a model having densities where is an unknown parameter. Find the MLE of . You do not have to prove that your solution is the global maximizer of the likelihood. It is enough to find

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Unformatted text preview: it. Problem 4 Suppose U and V are statistics that are both unbiased estimators of a parameter . Write and ,and define another statistic T = a U + (1 - a ) V where a is an arbitrary but known constant. a. Show that T is an unbiased estimator of . b. Find the a that gives T the smallest mean square error. Problem 5 Calculate the (expected) Fisher information for a model, where is an unknown parameter (i. e. ). Up: Stat 5132 Charles Geyer 1/2/1999...
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## This note was uploaded on 10/28/2010 for the course STAT 5101 taught by Professor Staff during the Spring '02 term at Minnesota.

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Stat 5132 (Geyer) Old First Midterm - it. Problem 4 Suppose...

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