Suppose that the regression model is y i = + i , where a. Given

Suppose that the regression model is y_i= μ + ε_i, where

a. Given a sample of observations on y_i and x_i, 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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E[e; |x;] = 0, Cov[s;, ɛ;|Xi, X;] = 0 for i = j, but Var[s; |x;] = o²x}, x; > 0.