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Explanatory Notes
Instructions
| XP33RSK |
Robust Statistics for Cybernetics |
| Roles: | S |
Extent of teaching: | 2P+0S |
| Department: | 13133 |
Language of teaching: | CS |
| Guarantors: | Nosková J. |
Completion: | ZK |
| Lecturers: | Nosková J. |
Credits: | 4 |
| Tutors: | Nosková J. |
Semester: | L |
Anotation:
Statistical methods are basic tools of control and decision making theory. Classical statistical methods (e.g. MLE) are usually very sensitive to deviations from our idealized model. Thus many methods which are robust have been developed. It means that these methods are not so sensitive to small deviations from an underlying model. So we briefly explain the parametric concept of estimation and then we introduce the robust approach, some basic robust estimators of location (e.g. trimmed mean, Hampel estimator) and measures of robustness (influence function, breakdown point).
Content:
| 1. | | Classical and robust statistics |
| 2. | | An estimation of location and scale |
| 3. | | The maximum likelihood estimation |
| 4. | | M-estimators of location |
| 5. | | Influence function |
| 6. | | Breakdown point |
| 7. | | M-estimators of scale |
| 8. | | Asymptotic normality of M-estimators |
| 9. | | Balancing bias and variance |
| 10. | | Hampel‘s optimality |
| 11. | | Linear model and LS method |
| 12. | | M-estimators in linear model |
| 13. | | Linear model with random predictors |
| 14. | | S-estimators(LTS) in linear model |
Course outlines:
Exercises outline:
Literature:
Ricardo A. Maronna, R. Douglas Martin, Victor J. Yohai, Matías Salibián-Barrera, Robust Statistics: Theory and Methods (with R), 2nd Edition
ISBN: 978-1-119-21466-3 October 2018 464 Pages
Rousseeuw,P.J., Leroy,A. (1987) Robust Regression and Outlier Detection.
Wiley, New York
Huber,P.J. (1981) Robust Statistics.Wiley,New York
Hampel,F.R.,Ronchetti, E.M.,Rousseeuw, P.J.,Stahel,W.A. (1986) Robust
Statistics: The Approach Based on Influence Functions. Wiley,New York
Dodge,Y., Jureckova,J. (2000) Adaptive Regression. Springer, New York
Requirements:
Subject is included into these academic programs:
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Proposal and Realization: I. Halaška (K336), J. Novák (K336) |