Answer to Question #264327 in Economics for lilu

Question

Explain what does the expression “OLS is BLUE” mean. State Gauss-Markov assumptions

required for OLS estimator to be BLUE.

Answer 1

In statistics, the Gauss-Markov theorem (or simply Gauss's theorem for some authors) states that a conventional least squares (OLS) estimate has the lowest sample variance in the class of linear unbiased estimates if the errors in the linear regression model are uncorrelated. , have equal variances and zero mathematical expectation. Errors do not have to be normal or independent and equally distributed (only uncorrelated with zero mean and homoscedastic with finite variance). The requirement that the estimate be unbiased cannot be waived as there are biased estimates with lower variance. See, for example, the James-Stein estimate (which also reduces linearity), ridge regression, or just any degenerate estimate.