Answer to Question #140663 in Statistics and Probability for Tunra

Question

Suppose that Q 1 , Q 2 , ∧ and Q 3 are ∧ estimators of ∧ θ. We know
∧
∧
that E ( Q 1 ) = E ( Q 2 ) = θ , E ( Q 3 ) ≠ θ ,V ( Q 1 ) = 12 , V ( Q 2 ) = 10 and
∧
E( Q 3 − θ ) 2 = 6 . Compare these three estimators. Which do you
prefer? Why?

Answer 1

Q₁ and Q₂ are better estimators of θ than Q₃, because the expected values of Q₁ and Q₂ are equal to θ, while the expected value of Q₃ is not equal to θ. Q₂ is a better estimator of θ than Q₁, because the estimators have the same expected value and Q₂ has a variance smaller than Q₁.