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Consider the simple regression yt = βxt + ε1 where E p[ε | x] = 0 and E [ε2 | x ] = σ2
(a) What is the minimum mean squared error linear estimator of β? Choose e to minimize Var [β] + [E(β – β)]2. The answer is a function of the unknown parameters].
(b) For the estimator in part a, show that ratio of the mean squared error of β to that of the ordinary least squares estimator b is Note that τ is the square of the population analog to the “t ratio” for testing the hypothesis that β = 0, which is given in (4-14). How do you interpret the behavior of this ratio as τ -> ∞? |
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