Non parametric statistics

Teacher(s)

Kiriliouk Anna;

Language

French
> English-friendly

Prerequisites

Concepts and tools equivalent to those taught in teaching unit LSTAT2014 : Eléments de probabilités et de statistique mathématique

Main themes

The themes of touched upon in the classroom are :
1.    Parametric vs nonparametric statistics
2.    Nonparametric estimation of a cumulative distribution function
3.    Location problems: the one-sample setting
4.    Location problems: the two-sample setting
5.    Location problems: the K-sample setting
6.    Dispersion problems: the two-sample setting
7.    Goodness of fit testing
8.    Association analysis

Learning outcomes

At the end of this learning unit, the student is able to :
1	The students will obtain knowledge about the basic concepts of nonparametric statistical inference. They will learn about elementary nonparametric testing procedures. They will be able to use these nonparametric procedures for analyzing real data, and this by using, for example, statistical software packages.

Content

The course focuses on the presentation of key concepts in nonparametric statistics, such as:

• Hypothesis tests concerning the location and dispersion of a population, based on an i.i.d. sample.
• Detection of differences in location and/or dispersion between two populations.
• Goodness-of-fit tests to determine whether an unknown distribution belongs to a parametric family of distributions or is equal to a specified distribution.
• Measures of association between two (or more) random variables.

Teaching methods

The course consists of lectures (15 hours) and exercise sessions (5 hours).
During the lectures, for each procedure, we explain the motivation behind the test statistic, how to derive the distribution of the test statistic under the null hypothesis, and how to carry out the test. The aim is for students to understand the reasoning underlying the various tests and to master the different steps involved in constructing a nonparametric test.

Evaluation methods

A three-hour written examination. The exam assesses your understanding of the course at a general level, including the motivation and interpretation of the different procedures, the choice of an appropriate procedure to answer specific practical questions, as well as calculations for small samples. A set of statistical tables will be provided both at the beginning of the semester and during the examination.

Online resources

Course Moodle site: LSTAT2140 – Nonparametric Statistics: Basic Methods
https://moodle.uclouvain.be/course/view.php?id=2756

Bibliography

• Gibbons, J.D. (1971). Nonparametric Statistical Inference. McGraw-Hill, New York.
• Hollander, M. et Wolfe, D.A. (1999). Nonparametric Statistical Methods. Second Edition. Wiley, New York.
• Lehmann, E.L. (1998). Nonparametrics: Statistical Methods Based on Ranks. Revised First Edition. Prentice Hall, New Jersey.
• Maritz. J.S. (1995). Distribution-free Statistical Methods. Second Edition. Chapman and Hall, New York.
• Mouchart, M. et Simar, L. (1978). Méthodes nonparamétriques. Recyclage en statistique, volume 2. Université catholique de Louvain, Louvain-la-Neuve, Belgique.
• Randles, R. et Wolfe, D. (1979). Introduction to the Theory of Nonparametric Statistics. Wiley, New York.

Teaching materials

• Transparents du cours disponible sur Moodle

Faculty or entity

> LSBA