Optimality and Asymptotics

This lecture discusses the optimality of the Least Squares Estimator (LSE) in the Gaussian Linear Model, showing that it is the best unbiased estimator. It explores the Gauss-Markov Theorem, which states that the LSE is the best linear unbiased estimator. The concept of optimality is further examined under weaker assumptions, focusing on uncorrelatedness. The lecture also delves into the large sample distribution of the estimator, emphasizing its behavior as the sample size grows. Various theorems and proofs are presented to support the discussion, shedding light on the distribution properties of the estimator under different conditions.