For the simple regression model y i = + i , i N[0,
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For the simple regression model yi = μ + εi, εi ∼ N[0, σ2], prove that the sample mean is consistent and asymptotically normally distributed. Now consider the alternative estimator μ̂ = Σi wi yi ,wi = i/(n(n+1)/2) = i/Σi i. Σi wi = 1. Prove that this is a consistent estimator of μ and obtain its asymptotic variance.
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The estimator is y 1 n i y i 1 n i i 1 n i i Then E y 1 n i E i and Vary 1 n 2 i j Cov i j 2 n Since ...View the full answer
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