Gauss–Markov Theorem

The Gauss–Markov theorem, named after German mathematician Carl Friedrich Gauss and Russian mathematician Andrey Markov, states that, under very general conditions, which do not include Gaussian assumptions, the ordinary least squares (OLS) method in linear regression models provides best linear unbiased estimators (BLUEs), a property that constitutes the theoretical justification for that widespread estimation method. This entry begins with a brief historical account of the Gauss–Markov theorem and then offers a review of least squares before undertaking an exploration of the Gauss–Markov theorem, including extensions of the theory as well as some of its limitations.