6 ECTS credits
150 h study time
Offer 1 with catalog number 4017231FNR for all students in the 2nd semester of odd academic years (e.g. 2013-2014) at a (F) Master - specialised level.
The course describes nonparametric dataprocessing tools which are frequently used throughout empirical research. Content:
1. Nonparametric tests for the two sample problem
The chapter revisits the two sample problem where classically the unpaired and paired t-tests are used if the data is drawn from a Gaussian distribution. This chapter describes a class of tests to tackle the two-sample problem robust to departures from the normality assumption. In particular, we treat: Wilcoxontoetsen, Mann-Whitneytoetsen, Wald-Wolfowitz and Kolmogorov-Smirnov tests.
2. Nonparametric one-way analysis of variance
This chapter revisits the one-way ANOVA designed by Fisher. Under the normality claim, the K-sample problem leads to the F-test to simultaneously test different means among groups. In the presence of departures of the normality assumption, the mean value is no longer sufficient which cannot serve as a leading statistic to design a hypothesis test. A one-way ANOVA which tests the equality of K-distributions is the Kruskal-Wallis ANOVA. A contrast ANOVA which assesses a monotonic location shift as a function of the groups is the Jonckheere-Terpstra ANOVA.
3. Sample size calculations for non-parametric tests.
To ensure that practical relevance and statistical significance coincide, one must compute the needed sample size. A sample size too large renders statistical significance for meaningless differences in practice by virtue of the weak law of large numbers, whereas a sample size too small is not able to verify the alternative hypothesis due to a lack of information.
4. Kernel density estimation and nonparametric regression
The histogram to visualize the density of the data is frequently used but the histogram holds mathematically poor properties. In this chapter, we derive a class of density estimators which improves the properties of the histogram. The kernel density estimators apply techniques from functional analysis where the density estimation problem is seen as an integral kernel problem. This idea is extended to tackle regression problems.
Syllabus is available in English. The course follows in part [J. Dickinson Gibbons en S. Chakraborti, Non-parametric statistical inference, ed. 5, CRP Press, 2011]. Technical details are added from scientific publications of the teacher.
Nonparametric methods are an important research field within the discipline of mathematical statistics. These methods are popular in applications where samples sizes are typically small (animal trials) or when the normality assumption is violated. The course provides an overview of nonparametric methods used in practice.
The final grade is composed based on the following categories:
Other Exam determines 100% of the final mark.
Within the Other Exam category, the following assignments need to be completed:
Oral examination with written preparation about the theory.
Per chapter, a group assignment with a written report of a maximal length of 10 A4 pages and presentation of its main results is requested. The group assignment consists of the statistical analysis of real life data with a dedicated research question or hypothesis.
Evaluation:
10 marks on exam.
4 group assignment with a maximal mark 4x5 evaluated through the presentations and reports. Differentiation among members of a group is possible at the oral examination where a discussion is held about the group assignments.
This offer is part of the following study plans:
Master of Mathematics: Financial and Applied Mathematics (only offered in Dutch)
Master of Mathematics: Education (only offered in Dutch)
Master of Teaching in Science and Technology: wiskunde (120 ECTS, Etterbeek) (only offered in Dutch)