Statistical theory

Summary

This course gives a mostly rigourous treatment of some statistical methods outside the context of standard likelihood theory.

Content

Keywords

Nonparametrics, inference, optimal transport, classification, shrinkage

Learning Prerequisites

Required courses

Courses on basic probability and statistics (e.g., MATH-240, MATH-230)

Recommended courses

Probability theory (MATH-432), Measures and integration (MATH-303)

Important concepts to start the course

Nothing specific is strictly necessary, but the pace will assume some level of mathematical and statistical maturity.

Learning Outcomes

• 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.

Expected student activities

Attending and actively interacting during lectures.

Assessment methods

Final written exam.

Supervision

Resources

Virtual desktop infrastructure (VDI)

No

Notes/Handbook

There will be lecture notes.

Moodle Link

• https://go.epfl.ch/MATH-442