Test_2_2007 - where d is a constant. Is an unbiased...

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Department of Economics Professor Dale J. Poirier University of California, Irvine December 11, 2007 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. Let f( @ ) > 0, and consider two random variables X 1 and X 2 distributed uniformly over C f = {x 1 , x 2 * 0 < x 1 < [f(x 2 /x 1 )] ½ }. Define (10) (a) What is the p.d.f. for y = x 2 /x 1 ? (10) (b) Suppose you wanted to generate a random variable with kernel equal to f( @ ). How could you easily do it? 2. Let Y t (t =1, 2, . .., T) be i.i.d. N( 2 , 2 2 ), 2 > 0. Denote the usual sample mean and variance estimators by and S 2 . Note that and cS are unbiased estimators of 2 , where (5) (a) Consider the estimator
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Unformatted text preview: where d is a constant. Is an unbiased estimator of 2 ? (10) (b) Find the value of d for which the MSE is minimized. (5) (c) Is [ , S 2 ] N a sufficient statistic for 2 ? (5) (d) Is [ , S 2 ] N a complete statistic? 2 (20) 3. Consider a random sample Y t (t =1, 2, . .., T) and define Express W in terms of the sample variance S 2 . [Hint: add zero judiciously.] 4. Let Y be a random variable with mean 2 and variance F 2 . Consider the estimator where a, b U . Assume quadratic loss. (5) (a) Suppose a &gt; 1. Is admissible? If so, show it. If not, show why not. (5) (b) Suppose a &lt; 0. Is admissible? If so, show it. If not, show why not. (5) (c) Suppose a = 1 and b 0. Is admissible? If so, show it. If not, show why not. (20) 5. Submit your computer homework problem....
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Test_2_2007 - where d is a constant. Is an unbiased...

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