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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 > 1. Is admissible? If so, show it. If not, show why not. (5) (b) Suppose a < 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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- Fall '10