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Unformatted text preview: E4708. Statistical Inference for FE. Professor S. Kou. Final Exam, Aug 26, 2009. Closed Book Exam . Total 50 pts. Note: For &true or falsequestions, simply answer &trueor &false. No explanation is needed. 1. (7 pts) Basic Facts from Empirical Finance. a. (2 pts) Null hypothesis: The defendant is innocent. Type I error: The defendant is innocent but the jury gives a guilty verdict. b. (1 pt) False. c. (2 pts) Kolmogorov-Siminov test and Jarque-Bera test. d. (1 pt)True e. (1 pt) False 2. (9 pts) The likelihoood for X 1 , ..., X n is given by f ( X j & ) = n Y i =1 e & & & X i X i ! : The prior density is & & 1 e & &= &( ) : Therefore, the posterior is given by f ( & j X ) _ & & 1 e & &= &( ) & n Y i =1 e & & & X i X i ! _ & & 1 e & &= & n Y i =1 e & & & X i = & & 1+ P n i =1 X i exp & 1 + n & : Thus, the posterior density f ( & j X ) must be a gamma with parameter ~ and ~ , where ~ = + n X i =1 X i ; ~ = 1 + n & 1 : And we can use the mean of the posterior as a Bayesian estimator, i.e. the estimator is ^ & = ~ ~ = + P n i =1 X i 1 + n = 1...
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This note was uploaded on 10/18/2010 for the course IEOR 4702 taught by Professor Kou during the Spring '10 term at Columbia.
- Spring '10