Syllabus
1. Classical and robust statistics - overview and main principles
2. Theoretical basics: the space of measures and its topology, functional derivatives
3. Statistical functional and its estimator, influence function, breakdown point
4. Basic types of estimators: M-estimators, Z-estimators, L-estimators, R-estimators
5. Minimax optimality of robust estimators of location
6. Further topics: Robust estimation of scale, robustness in regression, estimation for multidimensional data. Computational aspects.
Annotation
Robust statistics aims at methods that are suitable for data with possible outlying values. The goal of this course is to introduce the main principles of robust statistics.