Test_2_2005 - (5) (d) Find the sampling distribution of X-2...

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Department of Economics Professor Dale J. Poirier University of California, Irvine December 6, 2005 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. Let be an estimator of a vector 2 . Suppose is an inadmissible estimator of 2 with respect to quadratic loss. Can be a MSE consistent estimator of 2 ? If so, then provide an example. If not, why not? 2. Let Y = [Y 1 , Y 2 , . .., Y T ] N . Suppose Y * 2 , " 2 ~ t T ( 24 T , " 2 I T , 3). (5) (a) Find the sampling distribution of = (Y 1 + Y 2 + . .. + Y T )/T. (5) (b) Find the MSE of as an estimator of 2 . (5) (c) Find the sampling distribution of
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Unformatted text preview: (5) (d) Find the sampling distribution of X-2 . (5) (e) Does E(X-2 ) exist? If so, find it. If not, why not? 2 3. Consider Exercises 6.6.2(c) and 6.6.3(c) involving a random sample Y t (t = 1, 2, . .., T) from a distribution with p.d.f. f(y t * 2 ) = 2-1 exp(-y t / 2 ), 0 < y t < 4 , 0 < 2 < 4 . These exercises showed that was both the maximum likelihood and the method of moments estimator of 2 . (10) (a) Find (10) (b) Consider the estimator Find (10) (c) Compare the MSEs of and Which estimator has the lower MSE? 4. Let Y t (t = 1, 2, . .., T) be i.i.d. N( 2 , 2 2 ), 2 > 0. (10) (a) Show that X = [X 1 , X 2 ] N , where is a minimal sufficient statistic for 2 . (10) (b) Find (5) (c) Is X complete?...
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Test_2_2005 - (5) (d) Find the sampling distribution of X-2...

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