In: Economics
The Gauss Markov Theorem says
a) Under the LS assumptions, the OLS estimator has the smallest variance among all linear unbiased estimators
b) Under the LS assumptions, the OLS estimator has the smallest variance among all linear estimators
c) The OLS estimator has the smallest variance among all linear unbiased estimators
d) Under the LS assumptions, the OLS estimator is the most consistent estimator of all linear unbiased estimators
Solution-
The Gauss Markov Theorem says Under the LS assumptions, the OLS estimator has the smallest variance among all linear unbiased estimators.
The correct option is A. Under the LS assumptions, the OLS estimator has the smallest variance among all linear unbiased estimators.
Reason-
The Gauss-Markov Theorem states that, provided the Classical assumptions hold, the ordinary least squares (OLS) estimator b is the minimum variance estimator among all linear unbiased estimators.