Linear Models – MATH 341

Instructor: Prof. Victor Panaretos

Assistants: Alessia Caponera, Ho Yun

Moodle page of the course

Description

Regression modelling is a basic tool of statistics, because it describes how one variable may depend on another. The aim of this course is to familiarise students with the basics of regression modelling, and some related topics.

Topics covered include:

• Properties of the Multivariate Gaussian distribution and related quadratic forms.
• Gaussian linear regression: likelihood, least squares, variable manipulation and transformation, interactions.
• Geometrical interpretation, weighted least squares; distribution theory, Gauss-Markov theorem.
• Analysis of variance: F-statistics; sums of squares; orthogonality; experimental design.
• Linear statistical inference: general linear tests and confidence regions, simultaneous inference
• Model checking and validation: residual diagnostics, outliers and leverage points.
• Model selection: the bias variance effect, stepwise procedures. Information-based criteria.
• Multicollinearity and penalised estimation: ridge regression, the LASSO, relation to model selection, bias and variance revisited.
• Departures from standard assumptions: non-linear least Gaussian regression, robust regression and M-estimation.
• Nonparametric regression: kernel smoothing, roughness penalties, effective degrees of freedom, projection pursuit and additive models.

Required prior knowledge

The second-year course in statistics; first-year course in linear algebra

Recommended Texts

Draper, N.R. & Smith, H.S. (1998). Applied regression analysis. Wiley
Hocking, R.R. (1996). Methods and applications of linear models : regression and the analysis of variance. Wiley.
Davison, A.C. (2009).Statistical models. Cambridge.

Exam Information

There will be a written final exam.
No notes, books or any other material will be allowed in the exams.