3 The Gauss-Markov Theorem

Like any optimality result, it is crucial to lay out carefully the range of possiblealternatives, and the criterion by which those alternatives will be compared. Theclassical optimality result for estimating linear models is the Gauss-Markovtheorem, which takes the range of possibilities to be linear, unbiased estimatorsof β, and the criterion to be variance of the estimator. I will return to boththese choices at the end of this section.