The Coordinate-Free Approach to Gauss-Markov Estimation

Content -- § 1. Justification of the coordinate-free approach -- § 2. Vector-spaces -- a) Definition of a vector-space -- b) Inner products and semi-inner products -- c) Bases of a vector-space, orthogonal complement -- d) Linear functions, linear mappings and adjoint mappings -- e) Definition of set-operations in vector-spaces -- f) The Farkas’ theorem -- g) Projections, generalized inverses and pseudo-inverses -- § 3. Linear statistical models -- a) Definition of linear statistical models -- b) Least squares-estimators and Gauss-Markov estimators -- c) Supplements to least squares and Gauss-Markov estimation -- d) Examples: -- e) The estimation of ?2 -- f) Stepwise least squares and stepwise Gauss-Markov estimation.