# 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

12231

6.0

##### Responsible teacher

Filipe José Gonçalves Pereira Marques

##### Hours

Weekly - 4

Total - Available soon

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

Available soon

### Evaluation method

1. Pre-Requisites

In order to be able to have access to the course evaluation, both to midterms and tests and also to the Exam, students need to have the presence in at least 2/3 on the presential classes.

2. Evaluation

The recommended form of evaluation consists in:

1st Test - weight: 35%

2nd Test - weight: 35%

Project - weight: 30%

## 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

## Programs

Programs where the course is taught: