MD116 Robust and non-parametric methods II

Faculty of Science
Spring 2009
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. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 11:00–14:50 M3,01023
Prerequisites
Mathematical statistics, theory 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
Introduction to the classical estimation theory.
Basic concepts of the robustness: metrics on the space of probability distributions; statistical functional, its continuity and differentiability, derivatives.
Influence function, global and local sensitivities, breakdown point of the statistical functional.
Robust statistical estimation in the location and linear regression models.
At the end of this course, the students should be able to distinguish situations where they can use the classical estimates or where they should rather use the robust procedures. They should be able to recommend the type of the robust procedure, and apply it to the real data.
Syllabus
  • (1) Basic concepts of the theory of statistical estimation: loss and risk functions; convex loss function and reduction of the risk by means of a sufficient statistic, Rao-Blackwell and Lehmann-Scheffé theorems. (2) Translation and regression equivariance. Minimum risk equivariant estimator. Least squares estimator in the linear regression model. (3) 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. (4) Robust estimators of a scalar parameter, especially of the location parameter: and mutual relations. One-step versions of robust estimators. (5) 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. (6) Some goodness-of-fit tests in the presence of nuisance parameters of regression and scale. Extension of the Shapiro-Wilk test of normality.
Literature
  • Jurečková, Jana - Picek, Jan. Robust Statistical Methods with R. 1. vyd. Boca Raton, Florida, USA : Chapman & Hall/CRC, 2006. 197 s. ISBN 13:978-1-58488-454-5. info
  • Huber, Peter J. Robust statistical procedures. 5th print. Philadelphia : Society for Industrial and Applied Mathematics, 1989. 56 s. ISBN 0-89871-024-3.
Assessment methods
Lectures, oral exam
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 jaře 2009 probereme nejprve některé partie z klasické teorie statistického odhadu, hlavně odhady v regresním modelu a ekvivariantní odhady. Robustní odhady budou následovat.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2008.
  • Enrolment Statistics (recent)
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