In this lecture we will cover the Gauss-Markov theorem that establishes that out of the class of all linear unbiased estimators that the OLS estimator has minimum variance.
Readings: Christensen Chapter 2 and Chapter 6, Appendix A & B as needed C
In this lecture we will show that the MLEs are the best linear unbiased estimator through the Gauss-Markov Theorem and more generally under normality that they are the best unbiased estimator, where best means minimal variance. We will look at how this applies for optimal prediction as well as estimates of linear combinations of parameters.