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 2022
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer 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
Teaching methods:	full-time
Teaching methods:	full-time

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

Opinion survey results Examination dates SS schedule Noticeboard

Annotation -

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

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.

Aim of the course -

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

To understand principles of robust methods.

Course completion requirements -

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

Written and oral exam.

Literature -

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

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.

Teaching methods -

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

Lecture.

Requirements to the exam -

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

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

Syllabus -

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

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.

Entry requirements -

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

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