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Multivariate Models

Objectives

Acquire basic knowledge in multivariate statistics, particularly about the multivariate Normal and Wishart distributions, inference about mean vectors, multivariate regression, canonical analysis and introduction to copulas.
Use the concepts and techniques properly apprehended, along with the R software, in solving most diverse problems of real life.

General characterization

Code

12231

Credits

6.0

Responsible teacher

Filipe José Gonçalves Pereira Marques

Hours

Weekly - 4

Total - 56

Teaching language

Português

Prerequisites

Good knowledge of the subjects taught in Linear Algebra and in an introductory Course on Probabilities and Statistics.

Bibliography

Johnson, R. and Wichern, D. W. (2007), Applied Multivariate Statistical Analysis, 6th Edition, Prentice Hall, New Jersey.

Flury, B. (1997), A First Course in Multivariate Statistics, Springer. New York

Morrison, D. F. (2004), Multivariate Statistical Methods, 4th Edition, Duxbury Press

Rencher, A. C. (1998), Multivariate Statistical Inference and Applications, John Wiley & Sons

Rencher, A. C. (2002), Methods of Multivariate Analysis, John Wiley & Sons

Teaching method

Lectures, where the main concepts and results will be introduced to the students, together with the presentation of illustrative examples, which are intended to enlighten the concepts presented. These Lectures will be complemented with the resolution of problems with the help of an adequate computer software, related to the concepts introduced in the Lectures and will be made with the active participation of the students.

Evaluation method

 

1. Requirements

In order to be able to have admission the assessment of the subject, either by Continuous Assessment or by Exam, students must attend at least 2/3 of the classes.

 2. Evaluation 

Continuous Assessment consists of the following assessment elements:

1º Test - weight: 50%

2º Test - weight: 50%

Any student with a final mark (weighted average) of 9.5 or higher will be approved. Students who have not passed the continuous assessment may take an Exam if they meet the UC requirements.

Students who pass the continuous assessment can improve their grade in the Exam.

Students with a final mark of 18 or more must take an oral exam to defend their mark. If they don''t take this exam, they will receive a mark of 18.

 

Subject matter

1 - Brief reviews and basics of Linear Algebra
2 - The Multivariate Normal distribution. Maximum likelihood estimators and their distributions. The Wishart distribution
3 - Inference on vectors of averages
3.1 - Tests based on a sample
3.2 - Tests based on two samples, paired samples and independent samples
3.3 - Tests based on multiple samples
4 - Multivariate Regression and Canonical Analysis
5 - Introduction to Copulas
5.1 - Definition
5.2 - Dependence, Concordance, Upper and Lower tail dependencies
5.3 - The Guassian Copula
5.4 - The Archimedean family of copulas