Gauss-Markov Theorem: Optimal Estimation

This lecture covers the Gauss-Markov Theorem, which states that the Least Squares Estimators (LSE) are the best linear unbiased estimators in the Gaussian Linear model. It discusses the optimality properties of LSE under different assumptions, such as uncorrelatedness and normality. The lecture also explores the sampling distribution of LSE under moment assumptions and the large sample distribution of LSE. The Cramér-Wold device is used to prove the large sample distribution theorem. Additionally, the lecture delves into the asymptotic framework for covariates and the interpretation of the results in terms of the design's form.