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Last update: T_KPMS (26.04.2016)
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Last update: prof. RNDr. Jana Jurečková, DrSc. (06.10.2017)
To get acquainted with robust and nonparametric methods of statistics on rigorous mathematical background. |
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Last update: RNDr. Jitka Zichová, Dr. (31.05.2019)
Oral exam. |
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Last update: prof. RNDr. Jana Jurečková, DrSc. (06.10.2017)
Základní odborná literatura: J. Jurečková and J. Picek: Robust Statistical Methods with R. Chapman & Hall/CRC 2006 J. Hájek, Z. Šidák and P.K.Sen: Theory of Rank Tests. 2nd edition. Academic Press 1999.
Doporučená odborná literatura: J. Jurečková, P. K. Sen and J. Picek: Methodology in Robust and Nonparametric Statistics. Chapman & Hall/CRC, 2013. H. Oja: Multivariate Nonparametric Methods with R. An Approach Based on Spatial Signs and Ranks. Lecture Notes in Statistics 199, Springer 2010. P.J. Huber and E. M. Ronchetti: Robust Statistics. 2nd edition. J. Wiley 2009.
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Last update: prof. RNDr. Jana Jurečková, DrSc. (06.10.2017)
Lecture. |
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Last update: RNDr. Jitka Zichová, Dr. (31.05.2019)
Oral exam - according to sylabus. |
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Last update: prof. RNDr. Jana Jurečková, DrSc. (06.10.2017)
Part 1: Robust Statistical Methods 1. Differentiable statistical functionals, functional deriva tives. 2. Qualitative robustness. Quantitative characteristics of robustness. 3. Robust estimators of real parameter: M -estimators, L-estimators, R-estimators. 4. Robust estimators in linear model: Least squares method; M -estimators, influence function. Leverage points, GM-estimators. L-estimators, regression quantiles, regression rank scores. 5. Multivariate model: M-estimators of location and scatter, admissibility and shrinkage. 6. Some goodness-of-fit tests: Shapiro-Wilk test of normality with nuisance regression and scale.
Part 2: Nonparametric Statistical Methods 1. Invariant tests, order statistics and ranks, their behavior under the hypothesis of randomness. 2. Rank tests of randomness against two samples shift alternative: Wilcoxon test, van der Waerden test, median test. 3. Rank tests of randomness against two samples scale alternative: Siegel-Tukey test, quartile test. 4. Rank tests of randomness based on empirical distribution functions: Kolmogorov-Smirnov test, Cram´er -von Mises test. 5. Hypothesis of symmetry in a bivariate population. One-sample Wilcoxon test, sign test. 6. Hypothesis of independence in bivariate population and its alternatives. Spearman test, Kendall test, quadrant test. Spearman test against alternative of monotone trend. 7. Rank tests of randomness hypothesis against alternative of several samples. Kruskal-Wallis rank test and its application for categorical data. 8. Rank tests of homogeneity of several treatments under the block decomposition: Friedman test. 9. Rank tests under tied observations: Method of randomization, method of midranks. 10. Rank tests in the linear regression model; tests based on regression rank scores. |