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Suppose that the regression model is yi = μ + εi, where E[εi | xi ] = 0, Cov[εi, εj | xi , xj] = 0 for i ≠ j , but Var[εi | xi] = σ2x2i , xi > 0.
a. Given a sample of observations on yi and xi, what is the most efficient estimator of μ? What is its variance?
b. What is the OLS estimator of μ, and what is the variance of the ordinary least squares estimator?
c. Prove that the estimator in part a is at least as efficient as the estimator in part b. |
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