Summary

The course aims at developing certain key aspects of the theory of statistics, providing a common general framework for statistical methodology. While the main emphasis will be on the mathematical aspects of statistics, an effort will be made to balance rigor and intuition.

Content

Learning Prerequisites

Recommended courses

Real Analysis, Linear Algebra, Probability, Statistics.

Learning Outcomes

By the end of the course, the student must be able to:

• Formulate the various elements of a statistical problem rigorously.
• Formalize the performance of statistical procedures through probability theory.
• Systematize broad classes of probability models and their structural relation to inference.
• Construct efficient statistical procedures for point/interval estimation and testing in classical contexts.
• Derive certain exact (finite sample) properties of fundamental statistical procedures.
• Derive certain asymptotic (large sample) properties of fundamental statistical procedures.
• Formulate fundamental limitations and uncertainty principles of statistical theory.
• Prove certain fundamental structural and optimality theorems of statistics.

Teaching methods

Lecture ex cathedra using slides as well as the blackboard (especially for some proofs). Examples/exercises presented/solved at the blackboard.

Assessment methods

Final written exam.

Dans le cadre de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

Supervision

Resources

Notes/Handbook

The slides will be available on Moodle.