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Unformatted text preview: and S 2 . Note that and cS are unbiased estimators of 2 , where (5) (a) Consider the estimator 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 ? (10) (d) Is [ , S 2 ] N a complete statistic? 2 4. Suppose Z = [Z 1 , Z 2 , Z 3 ] N has the trinomial distribution M 3 (T, 2 ) with p.m.f. where 2 = [(1 - &quot; ) 2 , 2 &quot; (1 - &quot; ), &quot; 2 ] N and &quot; &gt; 0. (5) (a) What is the log-likelihood function for &quot; ? (10) (b) Find the MLE of &quot; . (5) (c) Find the Hessian for &quot; . (10) (d) Find the information for &quot; . (10) 5. Attach your answer to Question 2 of your computer homework assignment....
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This note was uploaded on 12/12/2010 for the course ECON ECON 220A taught by Professor Dalej.poirier during the Fall '10 term at UC Irvine.
- Fall '10