In this lecture we will cover prediction and optimal estimation/prediction and what quantities can be estimated or predicted.
Readings: Christensen Chapter 2 and Chapter 6, Appendix A & B as needed C
In this lecture we derive predictive distributions and will talk about optimal prediction and estimation using squared error loss or quadratic loss. We will extend estimation to the case where $X$ is not full rank and talk about what quantities can still be estimated uniquely from the data, a concept related to identifiability. 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.