Purpose

This course is the first part of the L3 statistics course, the second part being devoted to tests and model choice. It covers the fundamentals of parametric statistics, both from mathematical and methodological points of view. With some forays into computational statistics. The main theme is that modelling is an inherent part of the statistical practice, rather than an antecedent to the statistical step. Data may be a given, while models almost never are. This means one should keep a critical eye about models and develop critical tools to assess their adequation. Including, first and foremost, an assessment by simulation (Monte Carlo) methods.

As you may have noticed, the course is entirely in English, except for the partial and final exams. This means the practicals (TD) are in English as well and students are expected to communicate in English. There is indeed at least one course taught in English in each semester of the L3 and M1 years: Statistics (1) is the chosen course for the first semester of L3.

This year, some practicals (TP) will be included, covering R language programming and applications to the bootstrap methodology.

Contents

  1. Statistics, the what and why
  2. Probabilistic models for statistics
  3. Glivenko-Cantelli theorem, Monte Carlo principles, and the bootstrap 
  4. Likelihood function, geometry, and information
  5. Likelihood inference
  6. Bayesian inference

References

  • Wasserman, L. (2010) All of Statistics: A concise course in statistical inference. Springer-Verlag [Springer link, with discount code tCmCBtT43NBdmWr[amazon link]
  • Boos, D. and Stefanski, L.A. (2014) Essential statistical inference. Springer-Verlag
  • Cadre, B. et Vial. C. (2012) Statistique mathématique - cours et exercices corrigés. Ellipses [en français]

Documents

Instructors