Assignment07-2010 - as n 1 = x 1 1 n 1 + x 2 1 n 1 + x n 1...

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AEB 6571 - Econometric Methods I Assignment 7 Charles B. Moss October 15, 2010 1. Consider the our discussion on estimating the θ parameter from the Bernoulli density function. Extending to the scenario to n draws (from 2 draws) the probability density function for drawing k events (i.e., x k =1)is P [ k,n,θ ]= n k ! θ k (1 θ ) n - k . (1) Given this formulation, our estimator of θ was simply ˆ θ = k n . (2) SpeciFcally, S = k/ 1and T = k/ 2=( x 1 + x 2 ) / 2. Given this formula- tion, graph the MSE = E ± ˆ θ θ ² 2 for n =2 , 3 , 4. 2. Note that the estimators for n 1 and n 2 where n 2 = n 1 +1 can be written
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Unformatted text preview: as n 1 = x 1 1 n 1 + x 2 1 n 1 + x n 1 1 n 1 + x n 2 n 2 = x 1 1 n 2 + x 2 1 n 2 + x n 2 1 n 2 + x n 2 1 n 2 . (3) Demonstrate that MSE ( n 1 ) MSE ( n 2 ). 1 3. Prove the Central Limit Theorem using the characteristic function. Is this theorem applicable to the estimator of in Question 2? 4. Derive the Maximum Likelihood estimator for the parameter of the Bernoulli distribution. 2...
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This note was uploaded on 07/15/2011 for the course AEB 6180 taught by Professor Staff during the Spring '10 term at University of Florida.

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Assignment07-2010 - as n 1 = x 1 1 n 1 + x 2 1 n 1 + x n 1...

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