Linear Models

Course Code: ST 353; ST 454 | Credits: 4 | Prerequisite: Linear Algebra and Matrix Theory

Unit I:(Preliminaries) Review of linear algebra, orthogonal projection; random vectors and matrices; multivariate normal distribution (MVN) based on affine transformation; properties of MVN; sampling distributions; linear and quadratic forms.
Unit II:(The Full Rank Linear Model) Estimation and inference; the linear model; least square estimation; Gauss–Markov theorem; maximum likelihood estimation; estimation of σ²; MVUE.
Unit III:(Generalized Least Squares and Hypothesis Testing) Generalized least squares; over-fitting, under-fitting; model in centered form; estimated coefficient of determination; testing a subset of β; overall regression test; testing of general linear hypothesis; confidence and prediction intervals; analysis of variance models: the non-full rank case (e.g., ANOVA models), estimability and testability, parameterizations, and constraints.
Unit IV:(Sums of Squares) Breaking up sums of squares; types of sums of squares.

Apply advanced algebraic techniques in inference of linear models.
Apply different methods to estimate and test the relation between the independent and dependent variables.
Explain the concept and the method of generalized least squares.
Apply the method of generalized least squares for the treatment of any given set of data.
Test the general linear hypothesis, and construct confidence and prediction intervals.
Explain breaking up sums of squares and types of sums of squares with examples.

Rao, C. R. Linear Statistical Inference and Its Applications. 2nd ed. Wiley Eastern, 1973
Rao, A. R. and Bhimasankaram, P. Linear Algebra. 2nd ed. TRIM, Hindustan Book Agency, 2000
Sengupta, D. and Jammalamadaka, S. Rao. Linear Models: An Integrated Approach. World Scientific, 2003