Under what assumptions is the least squares estimator the best linear unbiased estimator?
In statistics, the Gauss–Markov theorem (or simply Gauss theorem for some authors) states that the ordinary least squares (OLS) estimator has the lowest sampling variance within the class of linear unbiased estimators, if the errors in the linear regression model are uncorrelated, have equal variances and expectation …
Is Least Squares an unbiased estimator?
The least squares estimates ˆβ are unbiased for β as long as ε has mean zero. Lemma 2.1 does not require normally distributed errors. It does not even make any assumptions about var(ε). To study the variance of ˆβ we will need assumptions on var(ε), but not on its mean.
Under which assumptions is the OLS estimator unbiased?
Under 1 – 5 (the Gauss-Markov assumptions) OLS is BLUE and efficient (as described above). Under 1 – 4, OLS is unbiased, and consistent.
What is the proof of the Gauss-Markov theorem?
The Gauss-Markov theorem states that if your linear regression model satisfies the first six classical assumptions, then ordinary least squares (OLS) regression produces unbiased estimates that have the smallest variance of all possible linear estimators. The proof for this theorem goes way beyond the scope of this blog post.
How is the OLS estimator related to Gauss-Markov?
The Gauss-Markov Theorem and “standard” assumptions Proof under what conditions the OLS estimator is unbiased Unbiased and Consistent Variance estimators of the OLS estimator, under different conditions Proof under standard GM assumptions the OLS estimator is the BLUE estimator Connection with Maximum Likelihood Estimation
Which is Gauss Markov estimator has the lowest sampling variance?
The Gauss-Markov (GM) theorem states that for an additive linear model, and under the ”standard” GM assumptions that the errors are uncorrelated and homoscedastic with expectation value zero, the Ordinary Least Squares (OLS) estimator has the lowest sampling variance within the class of linear unbiased estimators.
Which is the best OLS estimator under GM assumptions?
Under the GM assumptions, the OLS estimator is the BLUE (Best Linear Unbiased Estimator). Meaning, if the standard GM assumptions hold, of all linear unbiased estimators possible the OLS estimator is the one with minimum variance and is, therefore, most efficient. Let’s prove this: 6. Connection between OLS and Maximum Likelihood Estimation (MLE)