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Why is the OLS estimator blue?
OLS estimators are BLUE (i.e. they are linear, unbiased and have the least variance among the class of all linear and unbiased estimators). Each assumption that is made while studying OLS adds restrictions to the model, but at the same time, also allows to make stronger statements regarding OLS.
Which estimator is known as blue?
The Gauss-Markov Theorem states that if a linear regression model fulfils the assumptions of the classical linear regression model the ordinary least squares estimator is the best linear unbiased estimator (BLUE).
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 BLUE estimator under standard GM assumptions?
Proof under standard GM assumptions the OLS estimator is the BLUE estimator 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.
What does the best in blue mean in statistics?
The Best in BLUE refers to the sampling distribution with the minimum variance. That’s the tightest possible distribution of all unbiased linear estimation methods! As you can see, the best estimates are those that are unbiased and have the minimum variance.
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