MD115 Robust and non-parametric methods I

Faculty of Science
Autumn 2007
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
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
The course will be devoted to robust and nonparametric methods in linear regression model, and oriented mainly to the rank tests on the parameters of the linear model and to the robust point estimators of the parameters. The program can be modified according to the interest. 1. Hypotheses testing in the linear regression model (a) Summary of the classical methods: F-test and its power, analysis of variance. Literature: P. J. Bickel and K. A. Doksum: Mathematical Statistics: Basic Ideas and Selected Topics (the 1st edition 1977 Holden-Day, San Francisco). (b) Rank tests of the linear hypothesis: Rank tests on the slope and sign-rank tests on the intercept of the regression line. Tests on the parameters of the regression hyperplane. Relative asymptotic efficiency of the rank test with respect to the F-test. Literature: M. L. Puri and P. K. Sen: Nonparametric Methods in General Linear Models. J. Wiley, New York, 1985. (c) Rank tests in the linear model with random regressors and in the mixed models. Literature: M. L. Puri and P. K. Sen: Nonparametric Methods in General Linear Models. (d) Regression rank scores and regression quantiles: Tests on some components of the regression parameter with other components as nuisance. Literature: J. Jurečková and J. Picek: Robust Statistical Methods with R (Chapman & Hall 2005) J. Hájek, Z. Šidák and P. K. Sen: Theory of Rank Tests (Academic Press 2000). 2. Robust estimation in the linear regression model (following course MD116). Literature: J. Jurečková and J. Picek: Robust Statistical Methods with R (Chapman & Hall 2005) Y. Dodge and J. Jurečková: Adaptive Regression (Springer Verlag, New York 2000).
Syllabus
  • The course will be devoted to robust and nonparametric methods in linear regression model, and oriented mainly to the rank tests on the parameters of the linear model and to the robust point estimators of the parameters. The program can be modified according to the interest. 1. Hypotheses testing in the linear regression model (a) Summary of the classical methods: F-test and its power, analysis of variance. Literature: P. J. Bickel and K. A. Doksum: Mathematical Statistics: Basic Ideas and Selected Topics (the 1st edition 1977 Holden-Day, San Francisco). (b) Rank tests of the linear hypothesis: Rank tests on the slope and sign-rank tests on the intercept of the regression line. Tests on the parameters of the regression hyperplane. Relative asymptotic efficiency of the rank test with respect to the F-test. Literature: M. L. Puri and P. K. Sen: Nonparametric Methods in General Linear Models. J. Wiley, New York, 1985. (c) Rank tests in the linear model with random regressors and in the mixed models. Literature: M. L. Puri and P. K. Sen: Nonparametric Methods in General Linear Models. (d) Regression rank scores and regression quantiles: Tests on some components of the regression parameter with other components as nuisance. Literature: J. Jurečková and J. Picek: Robust Statistical Methods with R (Chapman & Hall 2005) J. Hájek, Z. Šidák and P. K. Sen: Theory of Rank Tests (Academic Press 2000). 2. Robust estimation in the linear regression model (following course MD116). Literature: J. Jurečková and J. Picek: Robust Statistical Methods with R (Chapman & Hall 2005) Y. Dodge and J. Jurečková: Adaptive Regression (Springer Verlag, New York 2000).
Literature
  • M. L. Puri and P. K. Sen: Nonparametric Methods in General Linear Models. J. Wiley, New York, 1985. J. Hájek, Z. Šidák and P. K. Sen: Theory of Rank Tests (Academic Press 2000). J. Jurečková and J. Picek: Robust Statistical Methods with R (Chapman & Hal
Assessment methods (in Czech)
Ústní zkouška
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 Autumn 2007 - for the purpose of the accreditation, Autumn 2008.
  • Enrolment Statistics (Autumn 2007, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2007/MD115