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Unformatted text preview: Economics 4261 Introduction to Econometrics Fall 2010 HOMEWORK 8 : GROUPS 7 ¡ 8, 10 ¡ 12 Question 1 Given that your likelihood function has a Poisson distribution with density f p θ q : (a) What distribution would you choose for your prior function, given the importance of conjugacy discussed in the lecture? Write down this function. (b) Combining the likelihood and the prior functions, solve for the posterior – what distribution does the posterior have? (c) The posterior contains information from the prior. Specify parameter values on the prior to make it as uninformative as possible. Given these values, what distribution does the posterior mimic? Question 2 Now assume your likelihood function is a Bernoulli distribution. (a) Using the Beta distribution as a prior, derive the form of the posterior. (b) What distribution family does the posterior belong to? Question 3 Under what conditions, will the weights obtained for the WLS estimator lead to an unbiased estimator? Under what conditions will the weights give a biased estimator? Finally, outline the relationships between the GLS, FGLS, WLS, and OLS estimators....
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This note was uploaded on 02/24/2011 for the course ECON 4261 taught by Professor Staff during the Spring '08 term at Minnesota.
- Spring '08