Subjects

Your browser does not support JavaScript, or its support is disabled. Some features may not be available.

Robust Statistical Methods - NMST444

Title:	Robustní statistické metody
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2024
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time
Is provided by:	NMSA602

Guarantor:	doc. Mgr. Stanislav Nagy, Ph.D.
Class:	M Mgr. PMSE M Mgr. PMSE > Povinně volitelné
Classification:	Mathematics > Probability and Statistics
Co-requisite :	NMSA407

Opinion survey results Examination dates WS schedule Noticeboard

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.

Last update: Omelka Marek, doc. Ing., Ph.D. (30.11.2020)

Aim of the course -

To understand principles of robust methods.

Last update: Omelka Marek, doc. Ing., Ph.D. (14.02.2023)

Course completion requirements -

Written and oral exam.

Last update: Zichová Jitka, RNDr., Dr. (03.06.2022)

Literature -

Huber, P. J.; Ronchetti, E. M. (2009). Robust statistics. Second edition. Wiley Series in Probability and Statistics. John Wiley & Sons, Inc., Hoboken, NJ. xvi+354 pp.

Jurečková, J. (2001). Robustní statistické metody. Karolinum.

Maronna, R. A.; Martin, R. D.; Yohai, V. J. (2006). Robust statistics: Theory and methods. Wiley Series in Probability and Statistic. John Wiley & Sons, Ltd., Chichester, xx+436 pp.

Last update: Nagy Stanislav, doc. Mgr., Ph.D. (07.11.2023)

Teaching methods -

Lecture.

Last update: Omelka Marek, doc. Ing., Ph.D. (03.12.2020)

Requirements to the exam -

The requirements for the oral exam are in agreement with the syllabus of the course as presented during lectures.

Last update: Omelka Marek, doc. Ing., Ph.D. (14.02.2023)

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.

Last update: Nagy Stanislav, doc. Mgr., Ph.D. (07.11.2023)

Entry requirements -

Basic knowledge of mathematical analysis, probability theory and mathematical analysis.

Last update: Nagy Stanislav, doc. Mgr., Ph.D. (07.11.2023)