Question

Suppose that instead of estimators of the form 𝑎𝑋+𝑒 , we consider estimators of the form Θˆ=𝑎𝑋 and ask for the value of 𝑎 that minimizes the mean squared error. Mimic the derivation you have just seen and find the optimal value of 𝑎 . Your answer should be an algebraic expression involving some of the constants 𝑏 , 𝑐 , 𝑑 , where 𝑏=𝐄[Θ2] , 𝑐=𝐄[Θ𝑋] , 𝑑=𝐄[𝑋2] .

Answer 1

c/d