# Test_2_2000 - Department of Economics University of...

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S 2 ' 1 T & 1 j T t ' 1 (Y t & ¯ Y ) 2 . ˆ θ ' ˆ θ 1 ˆ θ 2 ' Y 1 Y 2 and ˜ θ ' ˜ θ 1 ˜ θ 2 ' Y 1 Y 2 & Y 1 % Y 3 . Department of Economics Professor Dale J. Poirier University of California, Irvine December 7, 2000 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. Results from the text need not be reproduced in detail - you can merely cite the source. (25) 1. Suppose Y t (t = 1, 2, ..., T) - i.i.d. N(μ, σ 2 ). Let denote the sample mean, and let ¯ Y Determine the sign of the bias of the estimator S of the population standard deviation σ . 2. Suppose Y = [Y 1 , Y 2 , Y 3 ] N * θ - N 3 (μ, I 3 ), where θ = [ θ 1 , θ 2 ] N and μ = [ θ 1 , θ 2 , θ 1 ] N . Consider the following two estimators of θ : (15) (a) Compare and . Which estimator do you prefer? MSE( ˆ θ ) MSE( ˜ θ ) (10) (b) Let β = [1, c] θ , ,

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