MD116 Robust and non-parametric methods II

Faculty of Science
Spring 2008
Extent and Intensity
2/0. 2 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jana Jurečková, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Jana Jurečková, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 12:00–15:50 07011
Prerequisites
Mathematical statistics, teory of probability, linear models
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Robust statistical methods should work well not only under a specified distribution, but also in its neighborhood. We shall mainly concentrate on robust statistical estimation in the location and linear regression model, eventually in the multivariate statistical model.
Syllabus
  • (1) Basic concepts of robustness: Statistical functional, its continuity and derivatives on the metric space of probability distribution: Gateaux, Frechet and Hadamard derivatives. Influence function of the statistical functional and numerical characteristics of robustness based on the influence function: global and local robustness. Other characteristics of robustness: breakdown point, maxbias, tail behavior of the statistical functional. (2) Robust estimators of a scalar parameter, especially of the location parameter: and mutual relations. One-step versions of robust estimators. (3) Robust estimation in the linear regression model under random and nonrandom designs. M-, L-, R-estimators of the regression parameter vector, their influence functions and other properties. Regression quantiles and their applications. (3) Some goodness-of-fit tests in the presence of nuisance parameters of regression and scale. Extension of the Shapiro-Wilk test of normality.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course can also be completed outside the examination period.
The course is taught only once.
General note: Na podzim 2006 bude kurz zaměřen na odhady parametrů konečných populací a teorii statistického výběru.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2009.
  • Enrolment Statistics (Spring 2008, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2008/MD116