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Test_2_2002 - Department of Economics University of...

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V [Y 1 ¯ Y, Y 2 ¯ Y, . ..,Y T ¯ Y] Department of Economics Professor Dale J. Poirier University of California, Irvine December 10, 2002 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. (25) 1. Suppose, given θ , Y t (t = 1, 2, . .., T) are i.i.d. N( θ , σ 2 ). Assume σ 2 is known. Let where is the sample mean. Use V and Basu’s Theorem to argue that independence of ¯ Y and the sample variance S 2 . ¯ Y 2. Consider the homework problems Exercise 6.6.2(c) and Exercise 6.6.3(c) involving a random sample Y t (t = 1, 2, . .., T) from a distribution with p.d.f. f(y t θ ) = θ -1 exp(-y t / θ ), 0 < y t < , 0 < θ < . (20) (a) Show that a MVB estimator of θ exists and find its variance. (25) (b) Show that no MVB estimator of
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