Problem%20Set%2004_2010_2011[1]

Problem%20Set%2004_2010_2011[1] - Middle East Technical...

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ECON 206 1 Middle East Technical University 2010-2011 Fall Department of Economics ECON 206 Instructor: Ozan ERUYGUR Research Assistant: Pelin AKÇAGÜN PROBLEM SET 04 ESTIMATION – UNBIASEDNESS – MSE – CONFIDENCE INTERVALS PROBLEM 1 Suppose that   12 ˆˆ EE   ,   2 11 ˆ V and   2 22 ˆ V . Consider the estimator  31 2 ˆ 1 aa  . a) Show that 3 ˆ is an unbiased estimator for . b) If 1 ˆ and 2 ˆ are independent how should be constant a be chosen in order to minimize the variance of 3 ˆ ? PROBLEM 2 Suppose that , 3 , YYY denote a random sample from an exponential distribution with density function / 1 ,0 0, y ey fy elsewhere    . Consider the following estimators of : ˆ Y , 2 ˆ 2 YY , 3 2 ˆ 3 ,   41 2 3 ˆ min , , , 5 ˆ Y . a) Which of these estimators are unbiased? b) Among the unbiased estimators, which has the smallest variance? PROBLEM 3 The reading on a voltage meter connected to a test circuit is uniformly distributed over the interval ,1 , where is the true but unknown voltage of the circuit. Suppose that , , ..., n Y denotes a random sample of such readings. a) Show that Y is a biased estimator of , and compute the bias. b) Find a function of Y that is an unbiased estimator of . c) Find   MSE Y when Y is used as an estimator of .
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ECON 206 2 PROBLEM 4 An increase in the rate of consumer savings frequently is tied to a lack of confidence in the economy and is said to be an indicator of a recessional tendency in the economy. A random sampling of n = 200 savings accounts in a local community showed the mean increase in savings account values to be 7.2% over the past 12 months, with standard deviation 5.6%. Estimate the mean percentage increase in savings account values over the past 12 months for depositors in the community.
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Problem%20Set%2004_2010_2011[1] - Middle East Technical...

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