Maximum Likelihood estimation in linear models via projections.
In this lecture we will show how to use projection matrices to find the maximum likelihood estimates of $\beta$ in a Gaussian linear model, avoiding the use of derivatives, but instead taking a geometric approach.
Readings: Christensen Chapter 1-2, Appendex A & B
Matrix Algebra Review from StatSci Boot Camp
Please review the material in Chapter 1 of Christensen on expectations of vectors and matrices before class.