Test_2_2006 - Department of Economics University of...

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Department of Economics Professor Dale J. Poirier University of California, Irvine December 5, 2006 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. (20) 1. Consider a random sample Y t (t = 1, 2, ..., T) from a N( : , F 2 ) distribution with unknown mean and variance. Also consider the following loss function for estimating F 2 : Finally, consider estimators of the form for some constant d, where S 2 is the usual unbiased estimator of F 2 . Find the value of d which minimizes risk. (20) 2. Consider a random sample Y t (t = 1, 2, ..., T) from the gamma distribution G( " , $ ). Find a method of moments estimator of " and $ . 3. Suppose the opening prices per share X 1 and X 2 of two similar stocks are independent random variables with common density f X (x) = ½ exp[-½(x-4)], 4 < x <
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