- anglais uniquement
Linear Models - MATH 341
Instructor: Prof. Victor Panaretos
Assistants: Pavol Guričan,
- Exercise to hand in after Week 1: Exercise No. 2
- Exercise to hand in after Week 2: Exercise No. 2
- Exercise to hand in after Week 3: Exercise No. 1
- Exercise to hand in after Week 4: Exercise No. 4
- Exercise to hand in after Week 5: Exercise No. 1
- First practical is online, the deadline for submission is Monday November 21
- Exercise to hand in after Week 6: Exercise No. 2
- Exercise to hand in after Week 7: Exercise No. 2
- Exercise to hand in after Week 8: Exercise No. 4
- Exercise to hand in after Week 9: Exercise No. 3
- Exercise to hand in after Week 10: Exercise No. 2
- Second practical is online, the deadline for submission is Wednesday December 21
- 05/12: There was a small typo in exercise 1, the first line of code should have "PO56.txt" instead of "PO60.txt".
- Exercise to hand in after Week 11: Exercise No. 3
- Exercise to hand in after Week 12: Exercise No. 1
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
- Structuring a report (V.M. Panaretos)
- Advice on writing a report (A.C. Davison)
- Advice on writing a report (D.R. Brillinger)
- Writing technical papers or reports (A.S.C. Ehrenberg)
- Some useful notes on matrix calculus (from C.A. Felippa's online book)
- How to cite other people's work: citation.epfl.ch
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.
There will be a mock midterm exam (test blanc) and a written final exam.
No notes, books or any other material will be allowed in the exams.
The midterm will take place on Wednesday November 23rd, 16:15-18:00 in CM 3.
Each week one or two exercises will be graded to provide feedback. Deadline to hand these in is either at the beginning of the exercise session (following the week when they are set), or until 16:00 on the same Monday in the box outside of office MA B1 493.
Practicals aim at developing the practical skills required when applying regression methodology. Practicals are assigned on certain weeks and are due three weeks later.
Winter 2016 Schedule
|Exercises:||CH B3 31||Mondays, 16:15-18:00|
ExercisesSérie 1Corrigé 1
Série 2Corrigé 2
Série 3Corrigé 3
Série 4Corrigé 4
Série 5Corrigé 5
Série 6Corrigé 6
Série 7Corrigé 7
Série 8Corrigé 8
Série 9Corrigé 9
Série 10Corrigé 10
Série 11Corrigé 11
Série 12Corrigé 12
Série 13Corrigé 13