UCL - Multivariate probabilities ans statistics

[STAT2160]

[15h + 5h] 4 credits

Teacher(s): Ingrid Van Keilegom

Language: French

Level: Second

Aims
Main themes
Content and teaching methods
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Aims

By the end of this course, the student should be familiar with the basic concepts for modelling multivariate random experiments and should be able to develop the basic techniques of statistical inference (estimation and hypothesis testing) in these models. In particular, he/she should know the properties of multivariate normal distributions and of other associated distributions, needed for solving inference problems in multivariate populations.

Main themes

- Multivariate random variables, conditional expectation and linear approximation
- Multivariate normal vector
- Multivariate sampling and sampling distributions in relation to the normal law (Wishart, Hotelling)
- General principles of inference (maximum likelihood and likelihood ratio)
- Standard tests for multivariate normal populations (test for a mean, comparison of means, test with linear contraints, test for covariance matrices, ...).

Content and teaching methods

Content :
- Random vectors : joint, marginal and conditional distributions, independence, conditional expectation and covariance, best linear approximation.
- Limit theorems
- Normal vector : general properties and conditional properties
- Estimation for a multivariate normal distribution and sampling distribution of the estimators.
- Hypothesis testing for multivariate normal distributions : linear hypothesis in the marginal and conditional model, confidence intervals.

Method :
The course consists of lectures, meetings exercices and an individual project on computer.

Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Prerequisites
An elementary course on probability and statistics

Evaluation
The evaluation consists of :
- an oral exam
- a written exam (exercises)
- a project on computer

Teaching materials
The course notes will be distributed during the first lecture.

Professor
Ingrid Van Keilegom, tel. : 010/47 43 30,
e-mail : vankeilegom@stat.ucl.ac.be

References :
- Härdle, W. and L. Simar (2003), Applied Multivariate Statistical Analysis, manuscript, Humboldt-Universität zu Berlin, Berlin, to appear at Springer-Verlag, Berlin.
- Johnson, R.A. and D.W. Wichern (1988), Applied Multivariate Statistical Analysis}, Prentice Hall, London.
- Mardia, K.V., Kent, J.T. and J.M. Bibby (1979), Multivariate Analysis, Academic Press, Duluth, London.