Lectures on Least Squares Methods. Part I: Linear Least Squares

Detailed lectures on linear least squares.

1 Introduction: Prerequisites; Basic concepts and notation; General terminology for estimators
2 Ordinary Least Squares: Review of linear algebra; Ordinary Least Squares - OLS; Properties of the OLS estimator; Weighted least squares; Summary on the OLS estimator
3 LS solution of an under-determined linear system: A constrained optimization problem
4 Singular Value Decomposition: Review of linear algebra preliminary to SVD; Singular Value Decomposition - statement and proof
5 General LS solution for ANY linear system; Introduction to the general LS solution; The general LS solution; Geometrical interpretation of LS; Properties of the general LS estimator
6 Generalized Gauss-Markov theorem: Introduction; Estimable linear functions; Generalized Gauss-Markov theorem