Test_2_2003 - Department of Economics University of...

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Department of Economics Professor Dale J. Poirier University of California, Irvine December 9, 2003 FINAL EXAM ECON 220A Statistics and Econometrics I (open book) Directions : You must answer each of the following questions. Points (out of 100) are allocated as noted to the left of each question. Allocate your time according to these points. To receive any partial credit, you must show your work. 1. Suppose Y - N T ( : , E ) and denote its density by N T (y * : , E ). (10) (a) Find E Y| : , E [- R n{ N T (Y * : , E )}]. (10) (b) Find E Y| : , E [- R n{ N T (Y * $ , E )}] for some T×1 vector $ (not necessarily : ). 2. Suppose Y - N T ( : , E ), where : = 24 T , E = F 2 [(1 - " )I T + " 4 T 4 T N ], 4 T is a T×1 vector with each element equal to unity, and " > -(T-1) -1 . Note that all the diagonal elements of E are equal to
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Unformatted text preview: F 2 and all the off-diagonal elements of E are equal to "F 2 .. (5) (a) Under what circumstances does Y comprise a random sample? (10) (b) Find and simplify your answer. (10) (c) Is a MSE-consistent estimator of : for all " ? 3. Suppose Y t (t = 1, 2, . .., T) is a random sample from a N( : , F 2 ) distribution with F 2 known. (10) (a) Find the ML estimator of " / : 2 . (5) (b) Is and unbiased estimator of " ? (10) (c) Define / . Compare MSE( ) and MSE( ). (5) (d) Is the MVB estimator of " ? 2 (10) (e) Is the UMVU estimator of " ? (5) (f) Are there any undesirable properties of ? (10) (g) Suggest an estimator of " which dominates in MSE....
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