UCL - Probability and mathematical statistics

[STAT3100]

[30h] 6 credits

This course is taught in the 1st semester.

Teacher(s): Johan Segers, Ingrid Van Keilegom

Language: English

Aims
Main themes
Content and teaching methods
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Aims

This course covers the necessary tools in asymptotic statistics in order to perform modern research in statistics.

Main themes

The course covers the asymptotic theory in parametric inference, M- and Z- estimators, U-statistics, empirical processes and the functional delta method. In a second part of the course, these tools are applied in modern special topics of mathematical statistics such as, e.g., extreme value theory, ill-posed inverse problems,

Content and teaching methods

Contents
1. Stochastic convergence
2. Delta method and moment estimators
3. Projections and U-statistics
4. Empirical processes
5. M- and Z-estimators
6. Capita selecta on a modern research topic in statistics

Methods
Lectures
Take-home readings
Oral presentations by students

Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Prerequisites:
Analyse statistique (MATH2440)

Evaluation:
Oral presentations during the semester, and oral or written exam covering the lectures.

Support:
A syllabus and/or transparencies.
Supplementary literature:
Serfling, R. J. (1980) Approximation Theorems of Mathematical Statistics. Wiley, New York.
van der Vaart, A. (1998) Asymptotic Statistics. Cambridge University Press, Cambridge.