In statistics, the Gauss–Markov theorem, named after Carl
Friedrich Gauss and Andrey Markov, states that in a linear
regression model in which the errors have expectation zero, are
uncorrelated and have equal variances, the best linear
unbiased estimator(BLUE) of the
coefficients is given by the ordinary least
squares .
(OLS) estimator, provided it exists. Here "best" means giving
the lowest variance of the estimate, as compared to other unbiased,
linear estimators. The errors do not need to be normal, nor do they
need to be independent and identically distributed.The requirement
that the estimator be unbiased cannot be dropped, since biased
estimators exist with lower variance. See, for example, the
James–Stein estimato or ridge regression.